函数的分数阶矩和短间隔内两个平方和

IF 0.8 3区 数学 Q2 MATHEMATICS
Mathematika Pub Date : 2025-09-04 DOI:10.1112/mtk.70047
Siegfred Baluyot, Steven M. Gonek
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引用次数: 0

摘要

设它是两个完全平方和,否则。通过将方差与生成函数的二阶矩联系起来,研究了在短时间内的方差。本文提出了一种估计-函数分数阶矩的新方法,并将其应用于-函数的二阶矩来限定-函数的方差。我们的结果是有条件的黎曼假设的ζ函数和狄利克雷函数与非主字符模4。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Fractional moments of -functions and sums of two squares in short intervals

Fractional moments of -functions and sums of two squares in short intervals

Fractional moments of -functions and sums of two squares in short intervals

Let if is the sum of two perfect squares, and otherwise. We study the variance of in short intervals by relating the variance with the second moment of the generating function along . We develop a new method for estimating fractional moments of -functions and apply it to the second moment of to bound the variance of . Our results are conditional on the Riemann hypothesis for the zeta-function and the Dirichlet -function associated with the non-principal character modulo 4.

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来源期刊
Mathematika
Mathematika MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
1.40
自引率
0.00%
发文量
60
审稿时长
>12 weeks
期刊介绍: Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.
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