Character analogue of the Boole summation formula with applications
Number Theory
2017-10-16 v1
Abstract
In this paper, we present the character analogue of the Boole summation formula. Using this formula, an integral representation is derived for the alternating Dirichlet function and its derivative is evaluated at . Some applications of the character analogue of the Boole summation formula and the integral representation are given about the alternating Dirichlet function. Moreover, the reciprocity formulas for two new arithmetic sums, arising from utilizing the summation formulas, and for Hardy--Berndt sum are proved.
Keywords
Cite
@article{arxiv.1610.00965,
title = {Character analogue of the Boole summation formula with applications},
author = {Mümün Can and M. Cihat Dagli},
journal= {arXiv preprint arXiv:1610.00965},
year = {2017}
}