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SPECIAL VALUES OF THE RIEMANN ZETA FUNCTION CAPTURE ALL REAL NUMBERS.
- Source :
-
Proceedings of the American Mathematical Society . Sep2015, Vol. 143 Issue 9, p3743-3752. 10p. - Publication Year :
- 2015
-
Abstract
- It is shown that the set of odd values {ζ(3),ζ(5),...,ζ(2k +1),...} of the Riemann zeta function is rich enough to capture real numbers in an approximation aspect. Precisely, we prove that any real number can be strongly approximated by certain linear combinations of these odd values, where the coefficients belonging to these combinations are universal in the sense of being independent of ζ(n) for all integers n ≥ 2. This approximation property is reminiscent of the classical Diophantine approximation of Liouville numbers by rationals. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 143
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 103456610
- Full Text :
- https://doi.org/10.1090/S0002-9939-2015-12649-4