Accession Number : AD0748760

Title :   Bounds for Some Coefficients Related to the Zeta Function.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Rosser,J. Barkley

Report Date : JUL 1972

Pagination or Media Count : 24

Abstract : If one wishes to calculate numerical approximations for the Riemann zeta function in the critical strip, the most efficient procedure presently known is to use the Riemann-Siegel formula. This formula involves an asymptotic series. To be able to use it for the purposes of calculation, one must know a bound for the error if one uses T terms of the series. Such bounds have been given for the case where a single term is used. No bounds are given in the literature for larger values of T. In a subsequent article, such bounds will be given. To establish these, we need bounds on certain coefficients, (a sub n), appearing in the Riemann-Siegel formula. In the present article, such bounds are furnished. (Author)

Descriptors :   (*SPECIAL FUNCTIONS(MATHEMATICAL), APPROXIMATION(MATHEMATICS)), ASYMPTOTIC SERIES, INEQUALITIES, COMPUTER PROGRAMMING, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE