
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 RiemannSiegel 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 RiemannSiegel 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