Turkish Journal of Mathematics
DOI
10.3906/mat-1607-23
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.
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
