s = 0 时的巴恩斯-赫尔维茨zeta 循环和三角形的埃尔哈特准多项式

IF 0.5 3区数学 Q3 MATHEMATICS International Journal of Number Theory Pub Date : 2024-03-20 DOI:10.1142/s179304212450057x

Milton Espinoza

引用次数: 0

摘要

根据海耶斯的一个定理，我们给出了作者之前介绍的 PGL2(ℚ)上某些 1 循环在 s=0 时的特殊值的几何解释。这项工作产生了三个主要结果：我们的 s=0 处的循环的明确公式，海耶斯定理的概括和新证明，以及ℝ2 中某些三角形的埃尔哈特准多项式的第零系数的优雅求和公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

The Barnes–Hurwitz zeta cocycle at s = 0 and Ehrhart quasi-polynomials of triangles

Following a theorem of Hayes, we give a geometric interpretation of the special value at $s = 0$ of certain $1$ -cocycle on ${PGL}_{2} (ℚ)$ previously introduced by the author. This work yields three main results: an explicit formula for our cocycle at $s = 0$ , a generalization and a new proof of Hayes’ theorem, and an elegant summation formula for the zeroth coefficient of the Ehrhart quasi-polynomial of certain triangles in $ℝ^{2}$ .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.

期刊最新文献

Congruences for partial sums of the generating series for 3kk p-Adic hypergeometric functions and the trace of Frobenius of elliptic curves Translation functors for locally analytic representations On integers of the form p + 2a2 + 2b2 Almost prime triples and Chen's theorem