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Mathematics of Computation

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Calculation and applications of Epstein zeta functions

Author: Daniel Shanks
Journal: Math. Comp. 29 (1975), 271-287
MSC: Primary 10C15; Secondary 10-04, 10H10
Corrigendum: Math. Comp. 30 (1976), 900.
Corrigendum: Math. Comp. 30 (1976), 900.
Corrigendum: Math. Comp. 29 (1975), 1167.
Corrigendum: Math. Comp. 29 (1975), 1167.
MathSciNet review: 0409357
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Abstract: Rapidly convergent series are given for computing Epstein zeta functions at integer arguments. From these one may rapidly and accurately compute Dirichlet L functions and Dedekind zeta functions for quadratic and cubic fields of any negative discriminant. Tables of such functions computed in this way are described and numerous applications are given, including the evaluation of very slowly convergent products such as those that give constants of Landau and of Hardy-Littlewood.

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Article copyright: © Copyright 1975 American Mathematical Society