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

被引：0
|
作者：
Espinoza, Milton [1 ]
机构：
[1] Univ La Serena, Fac Ciencias, Dept Matemat, Juan Cisternas 1200, La Serena, Region De Coqui, Chile
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2024年 / 20卷 / 04期
关键词：
Barnes zeta function; Hurwitz zeta function; special values; group cocycles; rational polytopes; Ehrhart quasi-polynomials;
D O I：
10.1142/S179304212450057X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Double-struck capital R-2.
引用
收藏
页码：1141 / 1160
页数：20
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