Calculation and applications of Epstein zeta functions

Shanks, Daniel

doi:10.1090/S0025-5718-1975-0409357-2

Calculation and applications of Epstein zeta functions
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Math. Comp. 29 (1975), 271-287 Request permission

Corrigendum: Math. Comp. 30 (1976), 900.
Corrigendum: Math. Comp. 30 (1976), 900.
Corrigendum: Math. Comp. 29 (1975), 1167.
Corrigendum: Math. Comp. 29 (1975), 1167.

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.

References

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Lehrbuch der Algebra

Tables of Dirichlet L Functions and Dedekind Zeta Functions

Daniel Shanks and Larry P. Schmid, Variations on a theorem of Landau. I, Math. Comp. 20 (1966), 551–569. MR 210678, DOI 10.1090/S0025-5718-1966-0210678-1
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Abstracts of Short Communications

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J. Reine Angew. Math.

The

Class Groups of Non-Galois Cubic Fields

Daniel Shanks and Richard Serafin, Quadratic fields with four invariants divisible by $3$, Math. Comp. 27 (1973), 183–187. MR 330097, DOI 10.1090/S0025-5718-1973-0330097-0