Journal of Number Theory最新文献

英文中文

Torsion of rational elliptic curves over the Zp-extensions of quadratic fields 二次域zp扩展上有理椭圆曲线的扭转

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-08 DOI: 10.1016/j.jnt.2025.08.009

Ömer Avcı

Let E be an elliptic curve defined over

Q

. For a quadratic number field K and an odd prime number p, let L be a

Z_{p}

-extension of K. We prove that

E {(L)}_{tors} = E {(K)}_{tors}

when

p > 5

. It enables us to classify the groups that can be realized as the torsion subgroup

E {(L)}_{tors}

, by using the classification of torsion subgroups over the quadratic fields.

设E是定义在q上的椭圆曲线，对于二次数域K和奇素数p，设L是K的zp扩展，证明当p>；5时，E(L)tors=E(K)tors。利用二次域上扭转子群的分类，可以对可实现为扭转子群E(L)子群的群进行分类。

引用次数: 0

Galois theory of quadratic rational functions with periodic critical points 具有周期临界点的二次有理函数的伽罗瓦理论

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-08 DOI: 10.1016/j.jnt.2025.08.010

Özlem Ejder

Given a number field k, and a quadratic rational function

f (x) \in k (x)

, the associated arboreal representation of the absolute Galois group of k is a subgroup of the automorphism group of a regular rooted binary tree. Boston and Jones conjectured that the image of such a representation for

f \in Z [x]

contains a dense set of settled elements. An automorphism is settled if the number of its orbits on the nth level of the tree remains small as n goes to infinity.

In this article, we exhibit many quadratic rational functions whose associated Arboreal Galois groups are not densely settled. These examples arise from quadratic rational functions whose critical points lie in a single periodic orbit. To prove our results, we present a detailed study of the iterated monodromy groups (IMG) of f, which also allows us to provide a negative answer to Jones and Levy's question regarding settled pairs.

Furthermore, we study the iterated extension

k (f^{- \infty} (t))

generated by adjoining to

k (t)

all roots of

f^{n} (x) = t

for

n \geq 1

for a parameter t. We call the intersection of

k (f^{- \infty} (t))

with

\bar{k}

, the field of constants associated with f. When one of the two critical points of f is the image of the other, we show that the field of constants is contained in the cyclotomic extension of k generated by all 2-power roots of unity. In particular, we prove the conjecture of Ejder, Kara, and Ozman regarding the rational function

\frac{1}{{(x - 1)}^{2}}

给定一个数字域k，一个二次有理函数f(x)∈k(x)， k的绝对伽罗瓦群的关联树表示是正则根二叉树的自同构群的子群。Boston和Jones推测，对于f∈Z[x]，这样一个表示的像包含一个密集的固定元素集合。当n趋于无穷时，如果自同构在树的第n层上的轨道数仍然很小，则该自同构就成立了。在这篇文章中，我们展示了许多二次有理函数，其相关的树伽罗瓦群不是密集的。这些例子来自于临界点位于单一周期轨道上的二次有理函数。为了证明我们的结果，我们对f的迭代单群（IMG）进行了详细的研究，这也使我们能够对Jones和Levy关于固定对的问题提供否定的答案。进一步，我们研究了由相邻于k(t)的fn(x)=t的所有根（n≥1）对参数t产生的迭代扩展k（f−∞(t)）。我们称k（f−∞(t)）与k¯的交集为与f相关的常数域。当f的两个临界点之一是另一个临界点的像时，我们证明了常数域包含在由所有单位的2次方根产生的k的环形扩展中。特别地，我们证明了Ejder、Kara和Ozman关于有理函数1(x−1)2的猜想。

{"title":"Galois theory of quadratic rational functions with periodic critical points","authors":"Özlem Ejder","doi":"10.1016/j.jnt.2025.08.010","DOIUrl":"10.1016/j.jnt.2025.08.010","url":null,"abstract":"<div><div>Given a number field k, and a quadratic rational function <math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>∈</mo><mi>k</mi><mo>(</mo><mi>x</mi><mo>)</mo></math>, the associated arboreal representation of the absolute Galois group of k is a subgroup of the automorphism group of a regular rooted binary tree. Boston and Jones conjectured that the image of such a representation for <math><mi>f</mi><mo>∈</mo><mi>Z</mi><mo>[</mo><mi>x</mi><mo>]</mo></math> contains a dense set of settled elements. An automorphism is settled if the number of its orbits on the nth level of the tree remains small as n goes to infinity.</div><div>In this article, we exhibit many quadratic rational functions whose associated Arboreal Galois groups are not densely settled. These examples arise from quadratic rational functions whose critical points lie in a single periodic orbit. To prove our results, we present a detailed study of the iterated monodromy groups (IMG) of f, which also allows us to provide a negative answer to Jones and Levy's question regarding settled pairs.</div><div>Furthermore, we study the iterated extension <math><mi>k</mi><mo>(</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mo>∞</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></math> generated by adjoining to <math><mi>k</mi><mo>(</mo><mi>t</mi><mo>)</mo></math> all roots of <math><msup><mrow><mi>f</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>t</mi></math> for <math><mi>n</mi><mo>≥</mo><mn>1</mn></math> for a parameter t. We call the intersection of <math><mi>k</mi><mo>(</mo><msup><mrow><mi>f</mi></mrow><mrow><mo>−</mo><mo>∞</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></math> with <math><mover><mrow><mi>k</mi></mrow><mrow><mo>¯</mo></mrow></mover></math>, the field of constants associated with f. When one of the two critical points of f is the image of the other, we show that the field of constants is contained in the cyclotomic extension of k generated by all 2-power roots of unity. In particular, we prove the conjecture of Ejder, Kara, and Ozman regarding the rational function <math><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac></math>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"280 ","pages":"Pages 212-245"},"PeriodicalIF":0.7,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Abelian varieties with real multiplication: Classification and isogeny classes over finite fields 具有实乘法的阿贝尔变：有限域上的分类和同系类

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-05 DOI: 10.1016/j.jnt.2025.08.006

Tejasi Bhatnagar , Yu Fu

In this paper, we provide a classification of certain points on Hilbert modular varieties over finite fields under a mild assumption on Newton polygon. Furthermore, we use this characterization to prove estimates for the size of isogeny classes.

本文在牛顿多边形的温和假设下，给出了有限域上Hilbert模变体上某些点的分类。此外，我们使用这种表征来证明估计的大小等基因类。

引用次数: 0

Non-vanishing of a certain quantity related to the p-adic coupling of mock modular forms with newforms 仿模形式与新模形式的p进耦合关系到一定数量的不消失

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-05 DOI: 10.1016/j.jnt.2025.08.007

Pavel Guerzhoy

Several authors have recently proved results which express a cusp form as a p-adic limit of weakly holomorphic modular forms under repeated application of Atkin's U-operator. Initially, these results had a deficiency: one could not rule out the possibility when a certain quantity vanishes and the final result fails to be true. Later on, Ahlgren and Samart [1] found a method to prove the non-vanishing in question in the specific case considered by El-Guindy and Ono [10]. Hanson and Jameson [15] and (independently) Dicks [8] generalized this method to finitely many other cases.

In this paper, we present a different approach which allows us to prove a similar non-vanishing result for an infinite family of similar cases. Our approach also allows us to return back to the original example considered by El-Guindy and Ono [10], where we calculate the (manifestly non-zero) quantity explicitly in terms of Morita's p-adic Γ-function.

最近，几个作者在重复应用Atkin的u算子的情况下，证明了用弱全纯模形式的p进极限表示尖形的结果。最初，这些结果有一个缺陷：不能排除某一数量消失而最终结果不正确的可能性。后来，Ahlgren和Samart[1]找到了一种方法来证明El-Guindy和Ono[1]所考虑的特定情况下的不消失性。Hanson和Jameson[8]和Dicks[8]（独立地）将这种方法推广到有限的许多其他情况。在本文中，我们提出了一种不同的方法，它允许我们证明一个类似的不消失的结果对于无限族的类似情况。我们的方法还允许我们回到El-Guindy和Ono[10]所考虑的原始示例，其中我们根据Morita的p进Γ-function明确地计算（明显非零）数量。

引用次数: 0

Monodromy of elliptic logarithms: Some topological methods and effective results 椭圆对数的单一性：一些拓扑方法和有效结果

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-05 DOI: 10.1016/j.jnt.2025.08.008

Francesco Tropeano

We study monodromy groups associated with elliptic schemes, examining the action induced by the fundamental group of the base via analytic continuation. We develop effective methods for investigating the relative monodromy group of elliptic logarithms and present explicit constructions of loops that simultaneously have trivial action on periods and non-trivial action on logarithms. We provide a new proof that the relative monodromy group of non-torsion sections has full rank. Our results include topological methods and effective techniques for analyzing the ramification locus of sections.

研究与椭圆型方案相关的单群，通过解析延拓检验了基群对椭圆型方案的作用。我们发展了研究椭圆对数的相对单调群的有效方法，并给出了同时对周期有平凡作用和对对数有非平凡作用的环的显式构造。给出了非扭转截面的相对单群是满秩的一个新的证明。我们的结果包括拓扑方法和有效的技术来分析分支轨迹的部分。

引用次数: 0

On the moments of averages of Ramanujan sums 关于拉马努金和的平均矩

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-04 DOI: 10.1016/j.jnt.2025.08.002

Shivani Goel , M. Ram Murty

Chan and Kumchev studied averages of the first and second moments of Ramanujan sums. In this article, we extend this investigation by estimating the higher moments of averages of Ramanujan sums using a Tauberian theorem due to La Bretèche. We also give a result for the moments of averages of Cohen-Ramanujan sums.

Chan和Kumchev研究了拉马努金和的第一阶矩和第二阶矩的平均值。在本文中，我们扩展了这一研究，利用La bret的一个Tauberian定理估计了Ramanujan和的平均高矩。我们也给出了Cohen-Ramanujan和的平均矩的一个结果。

引用次数: 0

Corresponding Abelian extensions of integrally equivalent number fields 积分等价数域的相应阿贝尔扩展

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-04 DOI: 10.1016/j.jnt.2025.08.001

Shaver Phagan

Extensive work has been done to determine necessary and sufficient conditions for a bijective correspondence of abelian extensions of number fields to force an isomorphism of the base fields. However, explicit examples of correspondences over non-isomorphic fields are rare. Integrally equivalent number fields admit an induced correspondence of abelian extensions. Studying this correspondence using idelic class field theory and linear algebra, we show that the corresponding extensions share features similar to those of arithmetically equivalent fields, and yet they are not generally weakly Kronecker equivalent. We also extend a group cohomological result of Arapura-Katz-McReynolds-Solapurkar and present geometric and arithmetic applications.

为了确定数域的阿贝尔扩展的对偶对应以强制基域同构，已经做了大量的工作。然而，非同构域上对应的显式例子很少。积分等价数域承认阿贝尔扩展的引申对应。利用理想类场论和线性代数研究了这种对应关系，证明了相应的扩展具有与算术等价场相似的特征，但它们不是一般的弱Kronecker等价。我们还推广了Arapura-Katz-McReynolds-Solapurkar的群上同结果，并给出了其几何和算术应用。

引用次数: 0

Bounds on the number of squares in recurrence sequences: y0 = b2 (I) 递归序列中平方数的界限：y0 = b2 (I)

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-04 DOI: 10.1016/j.jnt.2025.08.003

Paul M. Voutier

We continue and generalise our earlier investigations of the number of squares in binary recurrence sequences. Here we consider sequences,

{(y_{k})}_{k = - \infty}^{\infty}

, arising from the solutions of generalised negative Pell equations,

X^{2} - d Y^{2} = c

, where −c and

y_{0}

are any positive squares. We show that there are at most 2 distinct squares larger than an explicit lower bound in such sequences. From this result, we also show that there are at most 5 distinct squares when

y_{0} = b^{2}

for infinitely many values of b, including all

1 \leq b \leq 24

, as well as once d exceeds an explicit lower bound, without any conditions on the size of such squares.

我们继续并推广了先前关于二值递归序列中平方数的研究。这里我们考虑由广义负Pell方程X2 - dY2=c的解引起的序列（yk）k=−∞∞，其中−c和y0是任意正平方。我们证明了在这样的数列中，最多有两个不同的大于显下界的平方。由这个结果，我们还证明了当y0=b2时，当b的无穷多个值，包括所有1≤b≤24，以及当d超过一个显式下界时，不需要对这种正方形的大小有任何条件，最多有5个不同的正方形。

{"title":"Bounds on the number of squares in recurrence sequences: y0 = b2 (I)","authors":"Paul M. Voutier","doi":"10.1016/j.jnt.2025.08.003","DOIUrl":"10.1016/j.jnt.2025.08.003","url":null,"abstract":"<div><div>We continue and generalise our earlier investigations of the number of squares in binary recurrence sequences. Here we consider sequences, <math><msubsup><mrow><mo>(</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>k</mi><mo>=</mo><mo>−</mo><mo>∞</mo></mrow><mrow><mo>∞</mo></mrow></msubsup></math>, arising from the solutions of generalised negative Pell equations, <math><msup><mrow><mi>X</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>d</mi><msup><mrow><mi>Y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mi>c</mi></math>, where −c and <math><msub><mrow><mi>y</mi></mrow><mrow><mn>0</mn></mrow></msub></math> are any positive squares. We show that there are at most 2 distinct squares larger than an explicit lower bound in such sequences. From this result, we also show that there are at most 5 distinct squares when <math><msub><mrow><mi>y</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></math> for infinitely many values of b, including all <math><mn>1</mn><mo>≤</mo><mi>b</mi><mo>≤</mo><mn>24</mn></math>, as well as once d exceeds an explicit lower bound, without any conditions on the size of such squares.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"280 ","pages":"Pages 246-270"},"PeriodicalIF":0.7,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Erdős inequality for primitive sets Erdős原始集合的不等式

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-04 DOI: 10.1016/j.jnt.2025.08.004

Petr Kucheriaviy

<div><div>A set of natural numbers A is called primitive if no element of A divides any other. Let <math><mi>Ω</mi><mo>(</mo><mi>n</mi><mo>)</mo></math> be the number of prime divisors of n counted with multiplicity. Let <math><msub><mrow><mi>f</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow></msub><mfrac><mrow><msup><mrow><mi>z</mi></mrow><mrow><mi>Ω</mi><mo>(</mo><mi>a</mi><mo>)</mo></mrow></msup></mrow><mrow><mi>a</mi><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>a</mi><mo>)</mo></mrow><mrow><mi>z</mi></mrow></msup></mrow></mfrac></math>, where <math><mi>z</mi><mo>∈</mo><msub><mrow><mi>R</mi></mrow><mrow><mo>></mo><mn>0</mn></mrow></msub></math>. Erdős proved in 1935 that <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∑</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow></msub><mfrac><mrow><mn>1</mn></mrow><mrow><mi>a</mi><mi>log</mi><mo>⁡</mo><mi>a</mi></mrow></mfrac></math> is uniformly bounded over all primitive sets A. We prove a generalization of Erdős inequality which provides an analogous result for <math><msub><mrow><mi>f</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math>, when <math><mi>z</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math>. Furthermore, we study the supremum of <math><msub><mrow><mi>f</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math> over all primitive sets. We also discuss <math><msub><mrow><mi>lim</mi></mrow><mrow><mi>z</mi><mo>→</mo><mn>0</mn></mrow></msub><mo>⁡</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math>, which is a generalization of Dirichlet density. We study the asymptotics of <math><msub><mrow><mi>f</mi></mrow><mrow><mi>z</mi></mrow></msub><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></math>, where <math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>=</mo><mo>{</mo><mi>n</mi><mo>:</mo><mi>Ω</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>k</mi><mo>}</mo></math>. For <math><mi>z</mi><mo>=</mo><mn>1</mn></math> we find the next term in asymptotic expansion of <math><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>)</mo></math> refining the result of Gorodetsky, Lichtman, and Wong. We also study the supremum of <math><msub><mrow><mo>∑</mo></mrow><mrow><mi>a</mi><mo>∈</mo><mi>A</mi></mrow></msub><msup><mrow><mi>z</mi></mrow><mrow><mi>Ω</mi><mo>(</mo><mi>a</mi><mo>)</mo></mrow></msup><mo>/</mo><mi>a</mi></math> over all primitive subsets of <math><mo>[</mo><mn>1

如果自然数A中的任何元素都不能整除其他自然数，则称自然数A为本数。设Ω(n)为n具有多重性的质因数个数。设fz(A)=∑A∈AzΩ(A) A (log (A) z，其中z∈R>；0。Erdős在1935年证明了f1(A)=∑A∈A1alog (A)在所有原始集A上是一致有界的。我们证明了Erdős不等式的一个推广，对于z∈(0,2)时的fz(A)提供了一个类似的结果。进一步，我们研究了fz(A)在所有原始集合上的最优性。我们还讨论了limz→0 (A)，它是Dirichlet密度的推广。我们研究了fz（Pk）的渐近性，其中Pk={n：Ω(n)=k}。对于z=1，我们找到f1（Pk）的渐近展开中的下一项，改进了Gorodetsky， Lichtman和Wong的结果。我们还研究了∑a∈AzΩ(a)/a在[1，N]的所有原始子集上的最优性。

引用次数: 0

On the minimal denominator problem in function fields 关于函数域的最小分母问题

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-09-04 DOI: 10.1016/j.jnt.2025.08.005

Noy Soffer Aranov

We study the minimal denominator problem in function fields. In particular, we compute the probability distribution function of the random variable which returns the degree of the smallest denominator Q, for which the ball of a fixed radius around a point contains a rational function of the form

\frac{P}{Q}

. Moreover, we discuss the distribution of the random variable which returns the denominator of minimal degree, as well as higher dimensional and P-adic generalizations. This can be viewed as a function field generalization of a paper by Chen and Haynes.

研究了函数域中的最小分母问题。特别地，我们计算了随机变量的概率分布函数，该随机变量返回最小分母Q的程度，对于它，围绕一点的固定半径的球包含形式为PQ的有理函数。此外，我们还讨论了返回最小次分母的随机变量的分布，以及高维和p进的推广。这可以看作是Chen和Haynes论文的函数场推广。

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Journal of Number Theory

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀