Rocky Mountain Journal of Mathematics

Results on values of Barnes polynomials

Abdelmejid Bayad and Taekyun Kim

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In this paper, we investigate rationality of the Barnes numbers, and we find explicit good bounds for their denominators. In addition, we give Fourier expansion of Barnes polynomials and, from this study, we connect generalized Barnes numbers to values of Dirichlet $L$-function at non-negative integers.

Article information

Rocky Mountain J. Math., Volume 43, Number 6 (2013), 1857-1869.

First available in Project Euclid: 25 February 2014

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Zentralblatt MATH identifier

Primary: 11B68: Bernoulli and Euler numbers and polynomials 11B83: Special sequences and polynomials 11B99: None of the above, but in this section 11M32: Multiple Dirichlet series and zeta functions and multizeta values

Bernoulli numbers and polynomials Barnes numbers and polynomials Von Staudt theorem Dirichlet L -function. The present research has been conducted by a Research Grant of Kwangwoon University in 2011


Bayad, Abdelmejid; Kim, Taekyun. Results on values of Barnes polynomials. Rocky Mountain J. Math. 43 (2013), no. 6, 1857--1869. doi:10.1216/RMJ-2013-43-6-1857.

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