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, M, & DAĞLI, M. C (2017). Character analogue of the Boole summation formula with applications. Turkish Journal of Mathematics 41 (5): 1204-1223. https://doi.org/10.3906/mat-1607-23
