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SOME REMARKS ON THE RIEMANN ZETA FUNCTION AND PRIME FACTORS OF NUMERATORS OF BERNOULLI NUMBERS

Part of: Sequences and sets

Published online by Cambridge University Press:  12 December 2011

FLORIAN LUCA  and
AMALIA PIZARRO-MADARIAGA
FLORIAN LUCA*
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autonoma de México, C.P. 58089, Morelia, Michoacán, México (email: fluca@matmor.unam.mx)
AMALIA PIZARRO-MADARIAGA
Affiliation:
Departamento de Matemáticas, Universidad de Valparaiso, Chile (email: amalia.pizarro@uv.cl)
*
✉For correspondence; e-mail: fluca@matmor.unam.mx
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Abstract

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We prove that the sequence {log ζ(n)}n≥2 is not holonomic, that is, does not satisfy a finite recurrence relation with polynomial coefficients. A similar result holds for L-functions. We then prove a result concerning the number of distinct prime factors of the sequence of numerators of even indexed Bernoulli numbers.

Keywords

Riemann zeta functionnonholonomicityprimesBernoulli numbers

MSC classification

Secondary: 11B68: Bernoulli and Euler numbers and polynomials
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 216 - 223
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

F. L. was supported in part by project SEP-CONACyT 79685. A. P. was supported in part by project Fondecyt No. 11100260.

References

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