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
 EPrint:
 8+8 pages (English+Russian)