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Journal of Siberian Federal University. Mathematics & Physics, 2023, Volume 16, Issue 1, Pages 135–141
(Mi jsfu1063)
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Explicit formula for sums related to the generalized Bernoulli numbers
Brahim Mittouab a Department of Mathematics, University Kasdi Merbah Ouargla, Algeria
b EDPNL & HM Laboratory of ENS Kouba, Algeria
Abstract:
Let χ be a Dirichlet character modulo a prime number p⩾3 and let Bm(χ) (m=1,2,…) be the generalized Bernoulli numbers associated with χ. Explicit formulas for the sums: \sum_{\substack{\chi\mod p\\\chi(-1)=+1, \chi\neq\chi_0}}B_{m}(\chi)B_{n}(\overline{\chi})\text{ and }\sum_{\substack{\chi\mod p\\ \chi(-1)=-1}}B_{m}(\chi)B_{n}(\overline{\chi}) are given in this paper.
Keywords:
character sum, Dirichlet L-function, Bernoulli number, generalized Bernoulli number.
Received: 10.07.2022 Received in revised form: 16.09.2022 Accepted: 04.11.2022
Citation:
Brahim Mittou, “Explicit formula for sums related to the generalized Bernoulli numbers”, J. Sib. Fed. Univ. Math. Phys., 16:1 (2023), 135–141
Linking options:
https://www.mathnet.ru/eng/jsfu1063 https://www.mathnet.ru/eng/jsfu/v16/i1/p135
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Abstract page: | 66 | Full-text PDF : | 27 | References: | 21 |
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