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SOME REMARKS ON THE RIEMANN ZETA FUNCTION AND PRIME FACTORS OF NUMERATORS OF BERNOULLI NUMBERS
Published online by Cambridge University Press: 12 December 2011
Abstract
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.
MSC classification
- 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.
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