Journal of Number Theory最新文献

英文中文

Conditional estimates for L-functions in the Selberg class Selberg类中l -函数的条件估计

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-08-01 Epub Date: 2026-02-04 DOI: 10.1016/j.jnt.2025.12.014

Neea Palojärvi , Aleksander Simonič

Assuming the Generalized Riemann Hypothesis, we provide uniform upper bounds with explicit main terms for moduli of

(L^{'} / L) (s)

and

\log L (s)

for

1 / 2 + δ \leq σ < 1

, fixed

δ \in (0, 1 / 2)

and for functions in the Selberg class. We also provide estimates under additional assumptions on the distribution of Dirichlet coefficients of

L (s)

on prime numbers. Moreover, by assuming a polynomial Euler product representation for

L (s)

, we establish uniform bounds for

| 3 / 4 - σ | \leq 1 / 4 - 1 / \log \log (q_{L} | t |^{d_{L}})

| 1 - σ | \leq 1 / \log \log (q_{L} | t |^{d_{L}})

and

σ = 1

, and completely explicit estimates by assuming also the strong λ-conjecture.

假设广义黎曼假设，对于1/2+δ≤σ<；1，固定δ∈(0,1/2)和Selberg类函数，我们给出了模（L ' /L）(s)和log (L)(s)的一致上界和显式主项。我们还提供了在质数上L(s)的狄利克雷系数分布的附加假设下的估计。此外，通过假设L(s)的多项式欧拉积表示，我们建立了|3/4−σ|≤1/4−1/log (qL|t|dL), |−σ|≤1/log （qL|t|dL）和σ=1的一致界，并通过假设强λ-猜想完全显式估计。

引用次数: 0

Counting rational points on Hirzebruch–Kleinschmidt varieties over global function fields 全局函数域上Hirzebruch-Kleinschmidt变的有理点计数

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-08-01 Epub Date: 2026-02-06 DOI: 10.1016/j.jnt.2026.01.008

Sebastián Herrero , Tobías Martínez , Pedro Montero

Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of complete smooth split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where precise analytic properties of the corresponding height zeta functions can be given. As application, we obtain asymptotic formulas for the number of rational points of large height on each subvariety, with explicit leading constants and controlled error terms.

受Bourqui关于Hirzebruch曲面上反正则高度zeta函数的工作的启发，我们研究了全局函数域上具有Picard秩2的完全光滑分裂环型的高度zeta函数，以及与大度量线束相关的高度函数。我们证明了这些变量可以自然地分解为子变量的有限不相交并，在这个子变量中可以给出相应高度zeta函数的精确解析性质。作为应用，我们得到了各子簇上大高度有理点个数的渐近公式，具有显式的前导常数和控制误差项。

引用次数: 0

Direct and inverse problems for restricted signed sumsets 有限符号集合的正逆问题

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-08-01 Epub Date: 2026-02-05 DOI: 10.1016/j.jnt.2025.12.013

Raj Kumar Mistri, Nitesh Prajapati

<div><div>Let <math><mi>A</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>}</mo></math> be a nonempty finite subset of an additive abelian group G. For a positive integer h, the h-fold signed sumset of A, denoted by <math><msub><mrow><mi>h</mi></mrow><mrow><mo>±</mo></mrow></msub><mi>A</mi></math>, is defined as<math><msub><mrow><mi>h</mi></mrow><mrow><mo>±</mo></mrow></msub><mi>A</mi><mo>=</mo><mrow><mo>{</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>k</mi></mrow></munderover><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>:</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mo>{</mo><mo>−</mo><mi>h</mi><mo>,</mo><mo>…</mo><mo>,</mo><mn>0</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>h</mi><mo>}</mo><mspace></mspace><mtext>for</mtext><mspace></mspace><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi></mrow><mspace></mspace><mrow><mtext>and</mtext><mspace></mspace><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>k</mi></mrow></munderover><mrow><mo>|</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo></mrow><mo>=</mo><mi>h</mi><mo>}</mo></mrow><mo>,</mo></math> and the restricted h-fold signed sumset of A, denoted by <math><msubsup><mrow><mi>h</mi></mrow><mrow><mo>±</mo></mrow><mrow><mo>∧</mo></mrow></msubsup><mi>A</mi></math>, is defined as<math><msubsup><mrow><mi>h</mi></mrow><mrow><mo>±</mo></mrow><mrow><mo>∧</mo></mrow></msubsup><mi>A</mi><mo>=</mo><mrow><mo>{</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>k</mi></mrow></munderover><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><msub><mrow><mi>a</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>:</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mrow><mo>{</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow><mspace></mspace><mtext>for</mtext><mspace></mspace><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi></mrow><mspace></mspace><mrow><mtext>and</mtext><mspace></mspace><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>k</mi></mrow></munderover><mrow><mo>|</mo><msub><mrow><mi>λ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>|</mo></mrow><mo>=</mo><mi>h</mi><mo>}</mo></mrow><mo>.</mo></math> A direct problem for the sumset <math><msubsup><mrow><mi>h</mi></mrow><mrow><mo>±</mo></mrow><mrow><mo>∧</mo></mrow></msubsup><mi>A</mi></math> is to find the optimal size of <math><msubsup><mrow><mi>h</mi></mrow><mrow><mo>±</mo></mrow><mrow><mo>∧</mo></

设A={a1，…，ak}是可加性阿贝尔群g的非空有限子集。对于正整数h，定义A的h-fold有符号集合h±A为ash±A={∑i=1kλ λ ai:λi∈{−h，…，0，…，h}fori=1,2，…，and∑i=1k|λi|=h}，定义A的受限h-fold有符号集合h±∧A为ash±∧A={∑i=1kλ λ ai:λi∈{−1,0,1}fori=1,2，…，and∑i=1k|λi|=h}。sumset h±∧A的一个直接问题是用h和|A|求出h±∧A的最优尺寸。该sumset的反问题是确定当sumset h±∧A具有最优大小时底层集合A的结构。由于Bajnok和Matzke的缘故，有限阿贝群中的有符号集合有了一些已知的结果，但对于限制h-fold有符号集合h±∧A，即使在整数Z的加性群中，也没有多少已知的结果。在G=Z的情况下，Bhanja、Komatsu和Pandey研究了h=2,3和k的有符号集合h±∧A的问题，并推测了h≥4时的正逆结果。在本文中，我们证明了这些猜想。

引用次数: 0

Simply connectedness and hyperbolicity 简单的连通性和双曲性

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-08-01 Epub Date: 2026-02-03 DOI: 10.1016/j.jnt.2026.01.005

Carlo Gasbarri , Erwan Rousseau , Amos Turchet , Julie Tzu-Yueh Wang

We generalize to arbitrary dimension our previous construction of simply connected weakly-special but not special varieties. We show that they satisfy the function field and complex analytic part of Campana's conjecture. Moreover, we give examples, in any dimension, of smooth simply connected nonisotrivial projective varieties of general type that satisfy the function field Lang and Vojta conjectures with an explicit exceptional set.

我们将以往的单连通弱特殊而非特殊变体的构造推广到任意维。证明了它们满足Campana猜想的函数场和复解析部分。此外，我们还给出了在任意维上满足函数域Lang猜想和Vojta猜想的光滑单连通非等平凡的一般型射影变的例子。

引用次数: 0

Modular supercuspidal lifts of weight 2 重量2的模超尖头提升

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-08-01 Epub Date: 2026-02-06 DOI: 10.1016/j.jnt.2025.12.015

Iván Blanco-Chacón , Luis Dieulefait

Let

F / Q

be a totally real number field and

N

an ideal of its ring of integers of norm N. Let

p > \max {k + 1, 6}

be a prime totally split in F such that

p ∤ N

. For every even

k \geq 2

, define the

[F : Q]

-dimensional parallel weight

k = (k, . . ., k)

. Let

f \in S_{k} (Γ_{0} (N))

be any non CM Hilbert cuspidal Hecke eigenform. Assume that the residual representation

{\overline{ρ}}_{f, P}

has large image for some prime

P

over p in the field of definition of f. Under these conditions, we prove that there exists a lift of

{\overline{ρ}}_{f, P}

associated to a Hilbert modular cuspform

g \in S_{2} (N p^{2}, ϵ)

which is supercuspidal at each prime of F over p. We also give a proof of the corresponding statement for classical Hecke cuspforms. Such statement was already proved by Khare [23] with classical techniques. Finally, using our main result we give a corrigenda for [12], correctly inserting the micro good dihedral prime in the level.

设F/Q是一个全实数域，N是它的范数N的整数环的理想，设p>；max （k+1,6）是一个在F中完全分裂的素数，使得p∤N。对于每一个偶k≥2，定义[F:Q]维平行权k=（k，…，k）。设f∈Sk（Γ0(N)）为任意非CM Hilbert倒立Hecke特征型。假设剩余表示ρ f，P在f的定义域中对某个素数P / P有大像。在这些条件下，我们证明了存在一个与希尔伯特模尖形g∈S2（Np2, λ）相关的ρ f，P的升力，该升力在f / P的每个素数处都是超尖形。我们还证明了经典Hecke尖形的相应陈述。这种说法已经被哈雷·巴布用经典技术证明了。最后，利用我们的主要结果，我们给出了[12]的更正，正确地将微良二面体素数插入到关卡中。

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引用次数: 0

On the existence of zero-sum subsequences with length not divided by a given number 零和子序列的存在性，且子序列的长度不除以给定的数

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-07-01 Epub Date: 2026-01-20 DOI: 10.1016/j.jnt.2025.12.002

Weidong Gao , Xiao Jiang , Yuanlin Li , Huijuan Qi

Let G be a finite abelian group and k be an integer not dividing the exponent of G. We denote by

E_{k} (G)

the smallest positive integer l such that every sequence over G of length no less than l has a zero-sum subsequence of length not divisible by k. In this paper, we focus on determining

E_{k} (G)

for

G = C_{n}

, a cyclic group of order n. Specifically, we prove that

E_{k} (C_{n}) = ⌊ \frac{k}{k - 1} (n - 1) ⌋ + 1

for

k \in {3} \cup (⌈ \frac{n}{2} ⌉, n)

设G是一个有限阿贝尔群，k是一个不除G指数的整数，我们用Ek(G)表示最小的正整数l，使得G上每一个长度不小于l的序列都有一个长度不能被k整除的零和子序列。本文重点讨论了对于n阶循环群G=Cn确定Ek(G)。具体地，我们证明了对于k∈{3}∪(≤≤n2²，n), Ek(Cn)=⌊kk−1（n−1）⌋+1。

引用次数: 0

Multiple standard twists of L-functions l函数的多重标准扭曲

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-07-01 Epub Date: 2026-02-04 DOI: 10.1016/j.jnt.2026.01.003

J. Kaczorowski , A. Perelli

The standard twist of L-functions plays a fundamental role in the Selberg class theory. It is defined as an absolutely convergent Dirichlet series and admits meromorphic continuation beyond the half-plane of absolute convergence. Nowadays, the analytic properties of the standard twist

F (s, α)

of an L-function F are well-understood. For example, it has poles when the positive number α belongs to the so-called spectrum of F, and is entire otherwise. In this paper, for a given set

F = {F_{1}, \dots, F_{N}}

of L-functions and

s \in C^{N}

, we consider the multiple standard twist

F (s, α)

. This is defined initially on a certain half-space of

C^{N}

, and we describe its meromorphic continuation to the whole space. Results in the multidimensional case are, in many ways, analogous to those in the one-dimensional case. In particular, the spectrum of a multiple standard twist is relevant to the description of the set of poles of

F (s, α)

. There are also significant differences; for instance, in the structure of the singularities.

l函数的标准扭曲在塞尔伯格类理论中起着重要的作用。它被定义为一个绝对收敛的狄利克雷级数，并且在绝对收敛的半平面之外允许亚纯延拓。目前，l函数F的标准扭转F（s,α）的解析性质已经得到了很好的理解。例如，当正数α属于所谓的F的谱时，它具有极点，否则它是完整的。对于给定的l -函数集F={F1，…，FN}，且s∈CN，我们考虑多重标准扭转F（s,α）。这是在CN的某半空间上的初始定义，我们描述了它对整个空间的亚纯延拓。多维情况下的结果在许多方面类似于一维情况下的结果。特别是，多重标准扭转的谱与F（s,α）的极点集的描述有关。也有显著的差异；例如，在奇点的结构中。

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引用次数: 0

The distribution of square-free integers in arithmetic progressions with prime power moduli 素数幂模等差数列中无平方整数的分布

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-07-01 Epub Date: 2026-02-04 DOI: 10.1016/j.jnt.2026.01.006

Mingxuan Zhong , Tianping Zhang

Text

We obtain an asymptotic formula for the distribution of square-free integers

k \leq X

in an arithmetic progression

k \equiv a (\mod q)

uniformly for

q \leq X^{3 / 4 + 1 / 16 - Δ (n)}

, where

q = p^{n}

(a, q) = 1

and

Δ (n)

is a decreasing function of n. Specially, when

n \geq 5

, we can get

1 / 16 - Δ (n) \geq 1 / 1044

. Previously Hooley (1975) showed that the asymptotic formula holds for a positive proportion of moduli

q \leq X^{3 / 4 - ε}

, while for the first time Mangerel (2021) broke the well-known 3/4-barrier for

q \leq X^{3 / 4 + 1 / 1044 - ε}

in the case of square-free, smooth moduli. Our results break the 3/4-barrier again in another case of prime power moduli and improve upon the range of q from the work of Mangerel. As a direct application, we derive a new record for the upper bound of the least square-free integer in an arithmetic progression with prime power modulus.

Video

For a video summary of this paper, please visit https://youtu.be/Hq7jCPi1EjM.

本文得到了等差数列k≡a（modq）中k≤X的无平方整数k≤X的均匀分布的渐近公式，当q≤X3/4+1/16−Δ(n)时，其中q=pn, (a,q)=1， Δ(n)是n的降函数。特别地，当n≥5时，我们可以得到1/16−Δ(n)≥1/1044。之前，Hooley（1975）证明了渐近公式适用于模q≤X3/4−ε的正比例，而Mangerel（2021）首次打破了众所周知的3/4障碍，即在无平方光滑模q≤X3/4+1/1044−ε的情况下。在素数幂模的另一种情况下，我们的结果再次打破了3/4的障碍，并改进了Mangerel的工作q的范围。作为一个直接应用，我们得到了素数幂模等差数列中最小二乘自由整数上界的一个新记录。观看本文的视频摘要，请访问https://youtu.be/Hq7jCPi1EjM。

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引用次数: 0

Comparison of component groups of ℓ-adic and mod ℓ monodromy groups -一元群与模一元群的分量群的比较

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-07-01 Epub Date: 2026-02-03 DOI: 10.1016/j.jnt.2025.12.011

Boyi Dai, Chun-Yin Hui

Let

{ρ_{ℓ} : {Gal}_{K} \to {GL}_{n} (Q_{ℓ})}_{ℓ}

be a semisimple compatible system of ℓ-adic representations of a number field K that is arising from geometry. Let

G_{ℓ} \subset {GL}_{n, Q_{ℓ}}

and

{\hat{\underline{G}}}_{ℓ} \subset {GL}_{n, F_{ℓ}}

be respectively the algebraic monodromy group and the full algebraic envelope of

ρ_{ℓ}

. We prove that there is a natural isomorphism between the component groups

π_{0} (G_{ℓ})

and

π_{0} ({\hat{\underline{G}}}_{ℓ})

for all sufficiently large ℓ.

设{ρ r:GalK→GLn(Q r)} r是一个由几何产生的数字域K的r进表示组成的半简单相容系统。设g_1∧GLn， q_1和g_1∧GLn，F _1分别为ρ _1的代数单群和满代数包络。证明了对于所有足够大的r， π0（g_1）和π0（g_1）之间存在自然同构。

引用次数: 0

Larsen's conjecture for elliptic curves over Q with analytic rank at most one 解析秩最多为1的Q上椭圆曲线的Larsen猜想

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory

Pub Date : 2026-07-01 Epub Date: 2026-01-20 DOI: 10.1016/j.jnt.2025.12.001

Seokhyun Choi, Bo-Hae Im

We prove Larsen's conjecture for elliptic curves over

Q

with analytic rank at most 1. Specifically, let

E / Q

be an elliptic curve over

Q

. If

E / Q

has analytic rank at most 1, then we prove that for any topologically finitely generated subgroup G of

Gal (\overline{Q} / Q)

, the rank of E over the fixed subfield

{\overline{Q}}^{G}

\overline{Q}

under G is infinite.

证明了分析秩不超过1的Q上的椭圆曲线的Larsen猜想。具体地说，设E/Q是Q上的一条椭圆曲线。如果E/Q的解析秩不超过1，那么我们证明对于任何拓扑有限生成的Gal（Q /Q）的子群G，在G下Q的固定子域Q上E的秩是无穷大的。

引用次数: 0

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