Turkish Journal of Mathematics
Abstract
In this paper, we present the character analogue of the Boole summationformula. Using this formula, an integral representation is derived for thealternating Dirichlet $L$-function and its derivative is evaluated at $s=0$.Some applications of the character analogue of the Boole summation formula andthe integral representation are given about the alternating Dirichlet $L$-function. Moreover, the reciprocity formulas for two new arithmetic sums,arising from the summation formulas, and for Hardy--Berndt sum $S_{p}(b,c:\chi)$ are proved.
DOI
10.3906/mat-1607-23
Keywords
Boole summation formula, Dirichlet $L$-function, Hardy--Berndt sum, Bernoulli and Euler polynomials
First Page
1204
Last Page
1223
Recommended Citation
CAN, MÜMÜN and DAĞLI, MUHAMMET CİHAT
(2017)
"Character analogue of the Boole summation formula with applications,"
Turkish Journal of Mathematics: Vol. 41:
No.
5, Article 12.
https://doi.org/10.3906/mat-1607-23
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss5/12
