On universality in short intervals for zeta-functions of certain cusp forms

IF 0.9 3区数学 Q2 MATHEMATICS

Mathematica Slovaca Pub Date : 2024-07-01 DOI:10.1515/ms-2024-0045

Antanas Laurinčikas, Darius Šiaučiūnas

引用次数: 0

Abstract

In this paper, we consider universality in short intervals for the zeta-function attached to a normalized Hecke-eigen cusp form with respect to the modular group. For this, we apply a conjecture for the mean square in short interval on the critical strip for that zeta-function. The proof of the obtained universality theorem is based on a probabilistic limit theorem in the space of analytic functions.

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论某些顶点形式的zeta函数在短区间内的普遍性

在本文中，我们考虑了关于模组的归一化 Hecke-eigen cusp 形式所附 zeta 函数在短区间内的普遍性。为此，我们应用了关于该zeta函数临界带短区间均方的猜想。所得普遍性定理的证明基于解析函数空间中的概率极限定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematica Slovaca 数学-数学

CiteScore

2.10

自引率

6.20%

发文量

审稿时长

6-12 weeks

期刊介绍： Mathematica Slovaca, the oldest and best mathematical journal in Slovakia, was founded in 1951 at the Mathematical Institute of the Slovak Academy of Science, Bratislava. It covers practically all mathematical areas. As a respectful international mathematical journal, it publishes only highly nontrivial original articles with complete proofs by assuring a high quality reviewing process. Its reputation was approved by many outstanding mathematicians who already contributed to Math. Slovaca. It makes bridges among mathematics, physics, soft computing, cryptography, biology, economy, measuring, etc.　 The Journal publishes original articles with complete proofs. Besides short notes the journal publishes also surveys as well as some issues are focusing on a theme of current interest.