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Karatsuba, E. A.

On a method for constructing a family of approximations of zeta constants by rational fractions. (English. Russian original) Zbl 1387.11094

Probl. Inf. Transm. 51, No. 4, 378-390 (2015); translation from Probl. Peredachi Inf. 51, No. 4, 78-91 (2015).
Summary: We present a new method for fast approximation of zeta constants, i.e., values \(\zeta(n)\) of the , \(n \geq 2\), \(n\) is an integer, by rational fractions. The method makes it possible to fast approximate zeta constants and certain combinations of successive values of zeta constants by rational fractions. By choosing values of coefficients involved in the combinations, one can control the convergence rate of the approximations and the computation complexity for the zeta constants.

Cited in 1 Review
Cited in 2 Documents

MSC:

11Y60 Evaluation of number-theoretic constants
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11Y16 Number-theoretic algorithms; complexity
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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