Calculation and Applications of Epstein Zeta Functions

DOI10.2307/2005480zbMath0302.10035OpenAlexW4234285686MaRDI QIDQ4055731

Daniel Shanks

Publication date: 1975

Full work available at URL: https://doi.org/10.2307/2005480

Mathematics Subject Classification ID

Quadratic extensions (11R11) Cubic and quartic extensions (11R16) Zeta functions and (L)-functions of number fields (11R42) Primes in congruence classes (11N13) Distribution of primes (11N05) Hurwitz and Lerch zeta functions (11M35) General binary quadratic forms (11E16)

Related Items

Applications of the theory of modular forms to number theory ⋮ Dihedral quartic approximations and series for \(\pi\) ⋮ The value of \(L(1/2,\chi)\) for abelian L-functions of complex quadratic fields ⋮ Table errata: “Über die Lösung einiger unbestimmten Gleichungen vierten Grades” (Avh. Norske Vid. Akad. Oslo. I. 1934, no. 14. 1–35) by W. Ljunggren ⋮ The Mahler measure for \(K3\) hypersurfaces

Cites Work

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• On the Conjecture of Hardy & Littlewood concerning the Number of Primes of the Form n 2 + a
• The 3‐class groups of non‐Galois cubic fields—I
• On Epstein's zeta function
• Variations on a Theorem of Landau. Part I
• Generalized Euler and Class Numbers
• On Epstein's Zeta-function.
• Real zeros of the Dedekind zeta function of an imaginary quadratic field
• On the zeros of Epstein's zeta function
• Quadratic Fields with Four Invariants Divisible by 3
• Bateman's Constants Reconsidered and the Distribution of Cubic Residues
• Supplementary Data and Remarks Concerning a Hardy-Littlewood Conjecture
• The Calculation of Certain Dirichlet Series
• Polylogarithms, Dirichlet Series, and Certain Constants

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