Irrationality of values of the Riemann zeta function
Abstract
The paper deals with a generalization of Rivoal's construction, which enables one to construct linear approximating forms in 1 and the values of the zeta function \zeta(s) only at odd points. We prove theorems on the irrationality of the number \zeta(s) for some odd integers s in a given segment of the set of positive integers. Using certain refined arithmetical estimates, we strengthen Rivoal's original results on the linear independence of the \zeta(s).
- Publication:
-
Izvestiya: Mathematics
- Pub Date:
- June 2002
- DOI:
- 10.1070/IM2002v066n03ABEH000387
- arXiv:
- arXiv:math/0104249
- Bibcode:
- 2002IzMat..66..489Z
- Keywords:
-
- Mathematics - Number Theory;
- Mathematics - Classical Analysis and ODEs;
- Primary 11J72;
- Secondary 33C60
- E-Print:
- 8+8 pages (English+Russian)