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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

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