论文信息 - An approximate functional equation for Dirichlet L-functions

An approximate functional equation for Dirichlet L-functions

A new asymptotic formula is derived for the computation of Dirichlet L-functions, L(s,X), where s = σ + it. The formula is applicable for large values of t and it has been used on the Mercury computer at Manchester University to calculate the zeros of the L-functions with moduli 3 and 4 on the line Rs = ½. The results have been placed in the Royal Society Depository for Unpublished Mathematical Tables (no. 83).

Maurice Vincent Wilkes | M. Wilkes | Dame Davies | Dame Davies

[1] Carl Ludwig Siegel,et al. Contributions to the Theory of the Dirichlet L-Series and the Epstein Zeta-Functions , 1943 .

[2] D. H. Lehmer. Extended computation of the Riemann zeta-function , 1956 .

[3] The evalution of Dirichlet L-functions , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4] J. Miller,et al. Tables of the Riemann zeta function , 1961 .