- Turkish Journal of Mathematics
- Vol: 41 Issue: 5
- Character analogue of the Boole summation formula with applications
Character analogue of the Boole summation formula with applications
Authors : Mümün Can, Muhammet Cihat Dağli
Pages : 1204-1223
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Boole summation formula, Dirichlet $L$-function, Hardy--Berndt sum, Bernoulli and Euler polynomials