A few remarks on the values of the Bernoulli polynomials at rational arguments and some relations with ζ(2k + 1)
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Published:2021-12
Issue:4
Volume:27
Page:180-186
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ISSN:1310-5132
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Container-title:Notes on Number Theory and Discrete Mathematics
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language:
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Short-container-title:NNTDM
Author:
de Camargo André PierroORCID,
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de Oliveira Teruya Giulliano Cogui,
Abstract
A problem posed by Lehmer in 1938 asks for simple closed formulae for the values of the even Bernoulli polynomials at rational arguments in terms of the Bernoulli numbers. We discuss this problem based on the Fourier expansion of the Bernoulli polynomials. We also give some necessary and sufficient conditions for ζ(2k + 1) be a rational multiple of π2k+1.
Publisher
Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)