从反向波出发的一般多重德里赫利数列

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-04-23 DOI:10.1016/j.jnt.2024.03.020

Will Sawin

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引用次数: 0

摘要

我们给出了函数场 Fq(T)上多重狄利克特数列的公理化特征，概括了迪亚科努和帕索尔给出的一组公理。其中的关键公理，即素数幂的系数与系数之和的关系，正式化了钦塔的一个观察结果。通过将系数展示为显式反向剪切的迹函数，并利用反向剪切的性质，证明了满足这些公理的多重狄利克特数列的存在性。以这种方式定义的多重狄利克特数列包括许多以前在文献中出现过的特例。

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General multiple Dirichlet series from perverse sheaves

We give an axiomatic characterization of multiple Dirichlet series over the function field $F_{q} (T)$ , generalizing a set of axioms given by Diaconu and Pasol. The key axiom, relating the coefficients at prime powers to sums of the coefficients, formalizes an observation of Chinta. The existence of multiple Dirichlet series satisfying these axioms is proved by exhibiting the coefficients as trace functions of explicit perverse sheaves and using properties of perverse sheaves. The multiple Dirichlet series defined this way include, as special cases, many that have appeared previously in the literature.

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.