Zeta functions for ideal classes in real quadratic fields, at \(s=0\)

DOI10.1016/j.jnt.2012.02.003zbMath1276.11180OpenAlexW2057160496MaRDI QIDQ423630

Andrew Granville, András Biró

Publication date: 4 June 2012

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.02.003

zbMATH Keywords

real quadratic fieldszeta functionsspecial value

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Zeta functions and (L)-functions of number fields (11R42)

Related Items (5)

Class number one problem for a family of real quadratic fields ⋮ Polynomial behavior of special values of partial zeta functions of real quadratic fields at \(s = 0\) ⋮ On the rank of universal quadratic forms over real quadratic fields ⋮ The class number one problem for the real quadratic fields $\mathbb {Q}(\sqrt {(an)^2+4a})$ ⋮ Distribution of Class Numbers in Continued Fraction Families of Real Quadratic Fields

Cites Work

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• Brumer elements over a real quadratic base field
• Class number 2 problem for certain real quadratic fields of Richaud-Degert type
• The complete determination of narrow Richaud-Degert type which is not 5 modulo 8 with class number two
• \(L\)-functions at \(s=1\). III: Totally real fields and Hilbert's twelfth problem
• Evaluation of Dedekind sums, Eisenstein cocycles, and special values of \(L\)-functions
• Computation of partial zeta values at \(s=0\) over a totally real cubic field
• Mollin's conjecture
• Prime Producing Quadratic Polynomials and Class-Numbers of Real Quadratic Fields
• Yokoi's conjecture
• Chowla's conjecture

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