Congruences relating class numbers of quadratic orders and Zagier's sums

JOURNAL OF NUMBER THEORY

卷:227

Article

Mizuno, Yoshinori¹ 

[1] Tokushima Univ, Grad Sch Technol Ind & Social Sci, 2-1 Minami Josanjima Cho, Tokushima 7708506, Japan

关键词: Class numbers;    Hirzebruch sums;    Genus character L-functions;   

DOI  :  10.1016/j.jnt.2021.03.019

来源: Elsevier

【 摘 要 】

We prove a congruence modulo 16 relating the class numbers h(-4p), h(16p) of quadratic orders and Zagier's sum m(4p) associated to root 4p, when p equivalent to 1(mod 4) is a prime. This gives an analogy to Chua-Gunby-Park-Yuan's congruence established when p equivalent to 3 (mod 4), and generalizes a recent work by Cheng and Guo. In particular, when p equivalent to 1 (mod 4) is a prime, it is shown that the class number h(-4p) is divisible by 16 if and only if the Zagier sum m(4p) is divisible by 16. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free