Journal of Number Theory最新文献

英文中文

Iterated integrals and cohomology 迭代积分与上同调

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-27 DOI: 10.1016/j.jnt.2025.09.024

Kathrin Bringmann , Nikolaos Diamantis

We introduce an extension of the standard cohomology which is characterised by maps that fail to be classical cocycles by products of simpler maps. The construction is motivated by the study of Manin's noncommutative modular symbols and of false theta functions. We use this construction to obtain a cohomological interpretation of important iterated integrals that arise in that study. In another direction, our approach gives modular counterparts to the long-studied relations among multiple zeta values.

我们引入了标准上同调的一个扩展，它的特征是映射不是由更简单映射的乘积构成的经典环。该构造的动机是对Manin的非交换模符号和假θ函数的研究。我们使用这种结构来获得在该研究中出现的重要迭代积分的上同调解释。在另一个方向上，我们的方法给出了长期研究的多个zeta值之间关系的模对应物。

引用次数: 0

Bounds on bilinear sums of generalized Kloosterman sums over arbitrary sets 广义Kloosterman和在任意集合上的双线性和的界

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-24 DOI: 10.1016/j.jnt.2025.09.027

Sen Xu , Tianping Zhang

Text

We prove a new bound on bilinear forms with generalized Kloosterman sums by using the sum-product phenomenon in

F_{p}

, which reached the barrier

M N > p^{\frac{3}{4}}

for the more general situation and complements those obtained by Kowalski, Michel, and Sawin (2020). We also establish new estimates for bilinear forms with two variables from arbitrary subsets of

F_{p}

, which has expanded the range of

M, N

obtained by Xi (2023).

Video

For a video summary of this paper, please visit https://youtu.be/Q472zpufLEs.

本文利用Fp中的和积现象证明了广义Kloosterman和双线性形式的一个新界，该界在更一般的情况下达到了MN>；p34，并补充了Kowalski， Michel, and Sawin（2020）的结果。我们还从Fp的任意子集中建立了具有两个变量的双线性形式的新估计，这扩展了Xi（2023）得到的M，N的范围。观看本文的视频摘要，请访问https://youtu.be/Q472zpufLEs。

引用次数: 0

Hybrid subconvex bounds for GL3 × GL1 twisted L-functions and their applications GL3 × GL1扭转l函数的混合次凸界及其应用

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-22 DOI: 10.1016/j.jnt.2025.09.014

Fei Hou , GuangShi Lü

Let

P, M

be two primes such that

(P, M) = 1

. Let f be a Hecke newform of level P, and χ a primitive Dirichlet character modulo M. In this paper, we study the hybrid subconvexity problem for

L (s, {sym}^{2} f \otimes χ)

simultaneously in the level and conductor aspects. Among other things, we prove that the hybrid subconvex bound can be achieved, so long as

M^{ε} < P < M^{3 / 20}

. One of the key ingredients is that we develop the classical level aspect version of the Voronoĭ formula for the symmetric square lift in an alternative way by tracing back to its geometric nature. As the direct applications, we obtained the subconvex bound for

L (s, f \otimes f \otimes χ)

simultaneously in the level and conductor aspects and the non-obvious bound for the problem of distinguishing modular forms f and

f^{χ}

based on their first Fourier coefficients.

设P，M是两个质数满足（P，M）=1。设f为能级P的Hecke新形式，χ为原Dirichlet特征模m。本文同时研究了L（s,sym2f⊗χ）在能级和导体方面的混合次凸性问题。此外，我们证明了混合次凸界是可以实现的，只要Mε<；P<M3/20。其中一个关键因素是，我们通过追溯对称方形提升的几何性质，以另一种方式开发了vorono_公式的经典水平方面版本。作为直接应用，我们同时得到了L（s,f⊗f⊗χ）在能级和导体方面的次凸界，以及根据f和fχ的一阶傅里叶系数区分模形式问题的非明显界。

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引用次数: 0

On local representation densities of Hermitian forms and special cycles II 关于厄米特形式和特殊环的局部表示密度II

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-22 DOI: 10.1016/j.jnt.2025.09.020

Sungyoon Cho

In this paper, we prove that there are certain relations among representation densities and provide an efficient way to compute representation densities by using these relations. As an application, we compute certain arithmetic intersection numbers of special cycles on unitary Rapoport-Zink spaces and propose a conjecture on these.

本文证明了表示密度之间存在一定的关系，并利用这些关系提供了一种计算表示密度的有效方法。作为应用，我们计算了酉Rapoport-Zink空间上特殊环的若干算术交数，并给出了关于这些交数的一个猜想。

引用次数: 0

Equidistribution of realizable Steinitz classes for cyclic Kummer extensions 循环Kummer扩展的可实现Steinitz类的等分布

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-22 DOI: 10.1016/j.jnt.2025.09.022

Brody Lynch

Let ℓ be prime, and K be a number field containing the ℓ-th roots of unity. We use classical algebraic number theory and some analytic techniques to prove that the Steinitz classes of

Z / ℓ Z

extensions of K ordered by relative discriminant are equidistributed among realizable classes in the ideal class group of K. For

ℓ = 2

, this was proved by Kable and Wright using the deep theory of prehomogeneous vector spaces. Foster proved that Steinitz classes are uniformly distributed between realizable classes for tamely ramified elementary-m extensions using the theory of Galois modules; our approach eliminates this tameness hypothesis.

设r为素数，K为一个包含n个单位根的数域。我们利用经典代数数论和一些解析技术证明了K的Z/ Z的相对判别序的Z扩展的Steinitz类在K的理想类群中的可实现类之间是均匀分布的。对于r =2， able和Wright利用预齐次向量空间的深度理论证明了这一点。Foster利用伽罗瓦模理论证明了在纯分枝的初等-m扩展中，Steinitz类是均匀分布在可实现类之间的；我们的方法消除了这种驯服假说。

引用次数: 0

Constructing unramified extensions and Murphy's law for Galois deformation rings 构造伽罗瓦变形环的非分枝扩展和墨菲定律

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-22 DOI: 10.1016/j.jnt.2025.09.023

Andreea Iorga

In this paper, we prove that, under a technical assumption, any semi-direct product of a p-group G with a group Φ of order prime to p can appear as the Galois group of a tower of extensions

M / L / K

with the property that M is the maximal unramified p-extension of L, and

Gal (M / L) ≅ G

. A consequence of this result is that any local ring admitting a surjection to

Z_{3}

Z_{5}

Z_{7}

with finite kernel can be realized as a universal everywhere unramified deformation ring.

本文证明了在一个技术假设下，p群G与阶为素数到p的群Φ的任何半直积都可以表现为扩展塔M/L/K的伽罗瓦群，其性质是M是L的最大无分枝p扩展，且Gal(M/L) = G。这一结果的一个结果是，任何局部环允许有有限核的Z3、Z5或Z7的抛射，都可以被实现为一个普适的处处无分支变形环。

引用次数: 0

Greenberg's conjecture and Iwasawa module of real biquadratic fields I 实双二次域的Greenberg猜想与Iwasawa模1

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-22 DOI: 10.1016/j.jnt.2025.09.015

Mohamed Mahmoud Chems-Eddin

The main aim of this paper is to investigate Greenberg's conjecture for real biquadratic fields. More precisely, we propose the following problem:

What are real biquadratic number fields k such that

rank (A (k_{\infty})) = rank (A (k_{1}))

? where

A (k_{\infty})

is the 2-Iwasawa module of k and

A (k_{1})

is the 2-class group of

k_{1}

the first layer of the cyclotomic

Z_{2}

-extension of k. Moreover, we give several families of real biquadratic fields k such that

A (k_{\infty})

is trivial or isomorphic to

Z / 2^{n} Z

Z / 2 Z \times Z / 2^{n} Z

, where n is a given positive integer. The reader can also find some results concerning the 2-rank of the class group of certain real triquadratic fields.

本文的主要目的是研究实双二次场的格林伯格猜想。更准确地说，我们提出以下问题：什么是实双二次数域k，使得秩(A(k∞))=秩（A(k1)）？其中A（k∞）是k的2-Iwasawa模，A（k1）是k的环切z2扩展的第一层k1的2类群。此外，我们给出了若干实双二次域k的族，使得A（k∞）平凡或同构于Z/2nZ或Z/2Z×Z/2nZ，其中n是给定的正整数。读者还可以找到关于某些实数三二次域类群的2秩的一些结果。

引用次数: 0

Natural density of the sets associated to Siegel eigenvalues of a Siegel cusp form of degree 2 与二阶西格尔尖峰形式的西格尔特征值相关的集合的自然密度

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-21 DOI: 10.1016/j.jnt.2025.09.016

Prashant Tiwari , Lalit Vaishya

We prove explicit lower bounds for the natural density of the sets of primes p represented by a reduced form of negative discriminant D such that Siegel eigenvalues

λ_{F} (p)

of a Cuspidal Siegel eigenforms F of degree 2 satisfy

c_{1} < λ_{F} (p) < c_{2}

for the real numbers

c_{1}

and

c_{2}

. A similar result is also proved for the set of primes p represented by a reduced form of negative discriminant D such that

| λ_{F} (p) | > c

. Analogous results are also valid if one replaces natural density by Dirichlet density. Moreover, we deal with various kinds of quantitative results concerning the comparison between the normalized Siegel eigenvalues over the primes p represented by a reduced form of negative discriminant D, of two distinct cuspidal Siegel eigenforms for the full symplectic group of degree 2 which are not Saito–Kurokawa lifts.

我们证明了由负判别式D的约简形式表示的素数集p的自然密度的显式下界，使得二阶倒转西格尔特征形式F的西格尔特征值λF(p)对实数c1和c2满足c1<；λF(p)<c2。对于由负判别式D的简化形式表示的素数集p，也证明了一个类似的结果，使得|λF(p)|>c。如果用狄利克雷密度代替自然密度，也可以得到类似的结果。此外，我们还处理了非Saito-Kurokawa举升的2次全辛群的两个不同的倒向西格尔特征型在由负判别式D的简化形式表示的素数p上的归一化西格尔特征值的比较的各种定量结果。

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引用次数: 0

Elementary abelian Sylow subgroups of the multiplicative group 乘法群的初等阿贝尔西鲁子群

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-21 DOI: 10.1016/j.jnt.2025.09.021

S. Morales , G. Polanco , P. Pollack

Erdős and Pomerance have shown that

φ (n)

typically has about

\frac{1}{2} {(\log \log n)}^{2}

distinct prime factors. More precisely,

ω (φ (n))

has normal order

\frac{1}{2} {(\log \log n)}^{2}

. Since

φ (n)

is the size of the multiplicative group

{(Z / n Z)}^{\times}

, this result also gives the normal number of Sylow subgroups of

{(Z / n Z)}^{\times}

. Recently, Pollack considered specifically noncyclic Sylow subgroups of

{(Z / n Z)}^{\times}

, showing that the count of those has normal order

\log \log n / \log \log \log n

. We prove that the count of noncyclic Sylow subgroups that are elementary abelian of a fixed rank

k \geq 2

has normal order

\frac{1}{k (k - 1)} \log \log n / \log \log \log n

. So for example, (typically) among the primes p for which the p-primary component of

{(Z / n Z)}^{\times}

is noncyclic, this component is

Z / p Z \oplus Z / p Z

about half the time. Additionally, we show that the count of p for which the p-Sylow subgroup of

{(Z / n Z)}^{\times}

is not elementary abelian has normal order

2 \sqrt{π} \sqrt{\log \log n} / \log \log \log n

Erdős和Pomerance已经证明φ(n)通常有大约12(log (log))2个不同的质因数。更准确地说，ω(φ(n))的正规阶是12(log log)2。由于φ(n)是乘法群（Z/nZ） x的大小，因此该结果也给出了（Z/nZ） x的Sylow子群的正常数目。最近，Pollack特别考虑了（Z/nZ） x的非循环Sylow子群，证明了这些子群的数量具有正阶log (n) /log (n) log (n)。证明了固定秩k≥2的初等阿贝尔的非循环Sylow子群的计数具有正态阶为1k(k−1)log (log)log (n) /log (log)log (log)log (n)。例如，（典型地）在（Z/nZ） x的p初级分量是非循环的素数p中，这个分量大约有一半的时间是Z/pZ⊕Z/pZ。此外，我们证明了（Z/nZ） x的p- sylow子群不是初等阿贝尔的p的计数具有正规阶2πlog (log) log (n) /log (n) log (n) log (n) log (n) log (n)。

引用次数: 0

Remarks on the Boston's unramified Fontaine-Mazur conjecture 论波士顿未被证实的方丹-马祖尔猜想

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2025-10-21 DOI: 10.1016/j.jnt.2025.09.019

Yufan Luo

This paper studies Boston's generalization of the unramified Fontaine-Mazur conjecture for Galois representations. The first main result establishes that the conjecture can be verified by restricting to the cases of p-adic Galois representations and

F_{p} [[T]]

-adic representations. The second main result is a finiteness theorem for the associated unramified Galois deformation rings under certain conditions.

本文研究了伽罗瓦表示下未分枝的Fontaine-Mazur猜想的波士顿推广。第一个主要结果建立了该猜想可以通过限制p进伽罗瓦表示和Fp[[T]]进表示的情况来验证。第二个主要结果是在一定条件下相关的无分支伽罗瓦变形环的有限定理。

引用次数: 0

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