An analogue of Wilton's formula and values of Dedekind zeta functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:495

Article

Banerjee, Soumyarup¹  Chakraborty, Kalyan²  Hoque, Azizul³ 

[1] Indian Inst Technol Gandhinagar, Dept Math, Palaj 382355, Gandhinagar, India

[2] Kerala Sch Math, Kozhikode 673571, Kerala, India

[3] Rangapara Coll, Dept Math, Sonitpur 784505, Assam, India

关键词: Wilton's formula;    Dedekind zeta function;    Special values of Dedekind zeta function;    Riesz sums;    Nakajima dissection;   

DOI  :  10.1016/j.jmaa.2020.124675

来源: Elsevier

【 摘 要 】

J. R. Wilton obtained an expression for the product of two Riemann zeta functions. This expression played a crucial role to find the approximate functional equation for the product of two Riemann zeta functions in the critical region. We find analogous expressions for the product of two Dedekind zeta functions and then use these expressions to find some expressions for Dedekind zeta values attached to arbitrary real as well as quadratic number fields at any positive integer. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free