A restricted Epstein zeta function and the evaluation of some definite integrals

DOI10.4064/aa104-1-2zbMath1037.11023OpenAlexW2158239665MaRDI QIDQ4548870

Kenneth S. Williams, Habib Muzaffar

Publication date: 27 August 2002

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa104-1-2

zbMATH Keywords

binary quadratic formsgeneradefinite integralsChowla-Selberg formula

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) General binary quadratic forms (11E16) Exponential and trigonometric functions (33B10)

Related Items (11)

Parameterized families of polylog integrals ⋮ Explicit evaluations of log-log integrals ⋮ Arithmetic properties of the Herglotz-Zagier-Novikov function ⋮ Extended higher Herglotz functions. I: Functional equations ⋮ Arithmetic properties of the Herglotz function ⋮ Logarithmic integrals with applications to BBP and Euler-type sums ⋮ Genus character L‐functions of quadratic orders and class numbers ⋮ On the variance of squarefree integers in short intervals and arithmetic progressions ⋮ Congruences relating class numbers of quadratic orders and Zagier's sums ⋮ Kronecker's first limit formula, revisited ⋮ Series involving \(\psi(z)\) and \(\zeta(z, s)\) functions and evaluation of integrals

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