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RAMANUJAN SUMS AND THE BURGESS ZETA FUNCTION.
- Source :
-
International Journal of Number Theory . Dec2012, Vol. 8 Issue 8, p2069-2092. 24p. - Publication Year :
- 2012
-
Abstract
- The Mellin transform of a summatory function involving weighted averages of Ramanujan sums is obtained in terms of Bernoulli numbers and values of the Burgess zeta function. The possible singularity of the Burgess zeta function at s = 1 is then shown to be equivalent to the evaluation of a certain infinite series involving such weighted averages. Bounds on the size of the tail of these series are given and specific bounds are shown to be equivalent to the Riemann hypothesis [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17930421
- Volume :
- 8
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- International Journal of Number Theory
- Publication Type :
- Academic Journal
- Accession number :
- 82579493
- Full Text :
- https://doi.org/10.1142/S1793042112501187