Journal of Number Theory最新文献

英文中文

Corrigendum to “On certain maximal hyperelliptic curves related to Chebyshev polynomials” [J. Number Theory 203 (2019) 276–293]

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-30 DOI: 10.1016/j.jnt.2024.10.011

Saeed Tafazolian , Jaap Top

引用次数: 0

Period of the Ikeda-Miyawaki lift

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-22 DOI: 10.1016/j.jnt.2024.09.014

Tomoyoshi Ibukiyama , Hidenori Katsurada , Hisashi Kojima

In this paper, first we give a weak version of Ikeda's conjecture on the period of the Ikeda-Miyawaki lift. Next, we confirm this conjecture rigorously in some cases.

引用次数: 0

Rational configuration problems and a family of curves

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-22 DOI: 10.1016/j.jnt.2024.09.008

Jonathan Love

Given

, we consider the number of rational points on the genus one curve

H_{η} : y^{2} = {(a (1 - x^{2}) + b (2 x))}^{2} + {(c (1 - x^{2}) + d (2 x))}^{2} .

We prove that the set of η for which

H_{η} (Q) \neq \emptyset

has density zero, and that if a rational point

(x_{0}, y_{0}) \in H_{η} (Q)

exists, then

H_{η} (Q)

is infinite unless a certain explicit polynomial in

a, b, c, d, x_{0}, y_{0}

vanishes.

Curves of the form

H_{η}

naturally occur in the study of configurations of points in

R^{n}

with rational distances between them. As one example demonstrating this framework, we prove that if a line through the origin in

R^{2}

passes through a rational point on the unit circle, then it contains a dense set of points P such that the distances from P to each of the three points

(0, 0)

(0, 1)

, and

(1, 1)

are all rational. We also prove some results regarding whether a rational number can be expressed as a sum or product of slopes of rational right triangles.

引用次数: 0

On gamma factors of Rankin–Selberg integrals for U2ℓ × ResE/FGLn

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-22 DOI: 10.1016/j.jnt.2024.09.013

Kazuki Morimoto

In this paper, we prove the fundamental properties of gamma factors defined by Rankin-Selberg integrals of Shimura type for pairs of generic representations

(π, τ)

U_{2 ℓ} (F)

and

{GL}_{n} (E)

for a local field F of characteristic zero and a quadratic extension E of F. We also prove similar results for pairs of generic representations

(π, τ_{1} \otimes τ_{2})

{GL}_{2 ℓ} (F)

and

{GL}_{n} (F) \times {GL}_{n} (F)

. As a corollary, we prove that the gamma factors arising from Langlands–Shahidi method and our gamma factors coincide.

引用次数: 0

On the height of some generators of Galois extensions with big Galois group

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-22 DOI: 10.1016/j.jnt.2024.10.004

Jonathan Jenvrin

We study the height of generators of Galois extensions of the rationals having the alternating group

A_{n}

as Galois group. We prove that if such generators are obtained from certain, albeit classical, constructions, their height tends to infinity as n increases. This provides an analogue of a result by Amoroso, originally established for the symmetric group.

引用次数: 0

A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-22 DOI: 10.1016/j.jnt.2024.09.011

Annika Burmester

We present the τ-invariant balanced quasi-shuffle algebra

G^{f}

, whose elements formalize (combinatorial) multiple Eisenstein series as well as multiple q-zeta values. In particular,

G^{f}

has natural maps into these two algebras, and we expect these maps to be isomorphisms. Racinet studied the algebra

Z^{f}

of formal multiple zeta values by examining the corresponding affine scheme DM. Similarly, we present the affine scheme BM corresponding to the algebra

G^{f}

. We show that Racinet's affine scheme DM embeds into our affine scheme BM. This leads to a projection from the algebra

G^{f}

onto

Z^{f}

. Via the above natural maps, this projection corresponds to extracting the constant terms of multiple Eisenstein series or the limit

q \to 1

of multiple q-zeta values.

{"title":"A generalization of formal multiple zeta values related to multiple Eisenstein series and multiple q-zeta values","authors":"Annika Burmester","doi":"10.1016/j.jnt.2024.09.011","DOIUrl":"10.1016/j.jnt.2024.09.011","url":null,"abstract":"<div><div>We present the τ-invariant balanced quasi-shuffle algebra <math><msup><mrow><mi>G</mi></mrow><mrow><mi>f</mi></mrow></msup></math>, whose elements formalize (combinatorial) multiple Eisenstein series as well as multiple q-zeta values. In particular, <math><msup><mrow><mi>G</mi></mrow><mrow><mi>f</mi></mrow></msup></math> has natural maps into these two algebras, and we expect these maps to be isomorphisms. Racinet studied the algebra <math><msup><mrow><mi>Z</mi></mrow><mrow><mi>f</mi></mrow></msup></math> of formal multiple zeta values by examining the corresponding affine scheme DM. Similarly, we present the affine scheme BM corresponding to the algebra <math><msup><mrow><mi>G</mi></mrow><mrow><mi>f</mi></mrow></msup></math>. We show that Racinet's affine scheme DM embeds into our affine scheme BM. This leads to a projection from the algebra <math><msup><mrow><mi>G</mi></mrow><mrow><mi>f</mi></mrow></msup></math> onto <math><msup><mrow><mi>Z</mi></mrow><mrow><mi>f</mi></mrow></msup></math>. Via the above natural maps, this projection corresponds to extracting the constant terms of multiple Eisenstein series or the limit <math><mi>q</mi><mo>→</mo><mn>1</mn></math> of multiple q-zeta values.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"269 ","pages":"Pages 106-137"},"PeriodicalIF":0.6,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142744128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uniform boundedness on rational maps with automorphisms

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-20 DOI: 10.1016/j.jnt.2024.09.012

Minsik Han

In this paper, we study the dynamical uniform boundedness conjecture over a family of rational maps with certain nontrivial automorphisms. Specifically, we consider a family of rational maps of an arbitrary degree

d \geq 2

whose automorphism group contains the cyclic group of order d. We prove that a subfamily of this family satisfies the dynamical uniform boundedness conjecture.

引用次数: 0

Galois actions on Tate modules of Abelian varieties with semi-stable reduction

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-20 DOI: 10.1016/j.jnt.2024.08.008

Khai-Hoan Nguyen-Dang

Let p be a rational prime number, let K denote a finite extension of

Q_{p}

\overline{K}

some fixed algebraic closure of K. Let

G_{K}

be the absolute Galois group of K and let

I_{K} \subset G_{K}

be its inertial subgroup. Let A be an Abelian variety defined over K, with semi-stable reduction. In this note, we give a criterion for which

V_{p} {(A)}^{I_{K}} = 0

, where

V_{p} (A)

is the p-adic Tate module associated to A.

引用次数: 0

First order Stickelberger modules over imaginary quadratic fields

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-20 DOI: 10.1016/j.jnt.2024.10.005

Saad El Boukhari

Let

K / k

be a finite abelian extension of number fields of Galois group G with k imaginary quadratic. Let

n \geq 2

be a rational integer, and for a certain finite set S of places of k, let

O_{K, S}

be the ring of S-integers of K. We use generalized Stark elements to construct first order Stickelberger modules in odd higher algebraic K-groups of

O_{K, S}

. We show that the Fitting ideal (resp. index) of these modules inside the corresponding odd K-groups is exactly the Fitting ideal (resp. cardinality) of the even higher algebraic K-group

K_{2 n - 2} (O_{K, S})

引用次数: 0

Counting wild quartics with prescribed discriminant and Galois closure group

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2024-11-20 DOI: 10.1016/j.jnt.2024.10.008

Sebastian Monnet

Given a 2-adic field K, we give a formula for the number of totally ramified quartic field extensions

L / K

with a given discriminant valuation and Galois closure group. We use these formulae to prove refinements of Serre's mass formula, which will have applications to the arithmetic statistics of number fields.

引用次数: 0

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.

﹀