CHARACTER ANALOGUES OF CERTAIN HARDY–BERNDT SUMS-Reference-Cited by-同舟云学术

CHARACTER ANALOGUES OF CERTAIN HARDY–BERNDT SUMS

Published:2014-03-18 Issue:03 Volume:10 Page:737-762
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

CAN MÜMÜN¹,KURT VELI¹

Affiliation:

1. Department of Mathematics, Akdeniz University, Antalya, TR-07058, Turkey

Abstract

In this paper we consider transformation formulas for [Formula: see text] We derive reciprocity theorems for the sums arising in these transformation formulas and investigate certain properties of them. With the help of the character analogues of the Euler–Maclaurin summation formula we establish integral representations for Hardy–Berndt character sums s3,p(d, c : χ) and s4,p(d, c : χ).

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042113501200

Reference19 articles.

1. Modular Functions and Dirichlet Series in Number Theory

2. Elementary proofs of Berndt’s reciprocity laws

3. Character transformation formulae similar to those for the Dedekind eta-function

4. Character analogues of the poisson and Euler-MacLaurin summation formulas with applications

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