Irrationality of values of the Riemann zeta function
By Wadim Zudilin. 2001
67 citations recorded by the source corpus.
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 ζ(s) only at odd points. We prove theorems on the irrationality of the number ζ(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 ζ(s).
Subfields: Algebra and Number Theory, Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/d9655baee4193be2949050b0e2ed3bf67b3ab353
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In Algebra and Number Theory
- Wadim Zudilin
- Victor J. W. Guo
- Ji-Cai Liu
- Holly Swisher
- Zhi-Wei Sun
- Jesús Guillera
- Armin Straub
- Su-Dan Wang
In Applied Mathematics
Citations in the corpus
- Arithmetic of linear forms involving odd zeta values (2002, methodology): “.1). But the same asymptotic problem can be solved directly on the basis of Lemma 5 with the use of the asymptotics of the gamma function and the saddle-point method. We refer the reader to [Ne1] and [Zu3], Sections 2 and 3, for details of this approach; here we only state the final result. Lemma 12.”