Kronecker's first limit formula, revisited

DOI10.1007/s40687-018-0138-0zbMath1441.11085OpenAlexW2795529709WikidataQ130028615 ScholiaQ130028615MaRDI QIDQ2319751

Özlem Imamoḡlu, William Duke, Árpad Tóth

Publication date: 20 August 2019

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40687-018-0138-0

zbMATH Keywords

CM pointsKronecker's first limit formula

Mathematics Subject Classification ID

Quadratic extensions (11R11) Forms of half-integer weight; nonholomorphic modular forms (11F37) Holomorphic modular forms of integral weight (11F11) Class numbers, class groups, discriminants (11R29)

Related Items (13)

Farey boat: continued fractions and triangulations, modular group and polygon dissections ⋮ Concentration of closed geodesics in the homology of modular curves ⋮ The Manin-Drinfeld theorem and the rationality of Rademacher symbols ⋮ A Kronecker limit formula for indefinite zeta functions ⋮ Modular invariants for real quadratic fields and Kloosterman sums ⋮ Genus character L‐functions of quadratic orders and class numbers ⋮ Transformation laws for generalized Dedekind sums associated to Fuchsian groups ⋮ Riesz means of certain arithmetic functions ⋮ Polyharmonic weak Maass forms of higher depth for \(\mathrm{SL}_2(\mathbb{Z})\) ⋮ Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers ⋮ Traces of CM values and cycle integrals of polyharmonic Maass forms ⋮ A simple evaluation of a theta value, the Kronecker limit formula and a formula of Ramanujan ⋮ Shintani theta lifts of harmonic Maass forms

Cites Work

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• Geometric invariants for real quadratic fields
• Cycle integrals of the \(j\)-function and mock modular forms
• scl.
• On determinants of Laplacians on Riemann surfaces
• A proof of the classical Kronecker limit formula
• Elliptic functions according to Eisenstein and Kronecker.
• Coding of closed geodesics after Gauss and Morse
• A Kronecker limit formula for real quadratic fields
• Hilbert modular surfaces
• Polyharmonic Maass forms for \(\mathrm{PSL}(2,\mathbb Z)\)
• Some applications of Kronecker's limit formulas
• Imaginäre quadratische Zahlkörper mit der Klassenzahl Eins
• L-Series, modular imbeddings, and signatures
• Values of \(L\)-functions at \(s=1\). I: \(L\)-functions for quadratic forms
• Analytic torsion for complex manifolds
• Modular cocycles and linking numbers
• Diophantine analysis and modular forms
• Higher Kronecker “limit” formulas for real quadratic fields
• On the analogue of the formula of Chowla and Selberg for real quadratic fields.
• A restricted Epstein zeta function and the evaluation of some definite integrals
• Immersed surfaces in the modular orbifold
• On Epstein's Zeta-function.
• On Epstein's Zeta Function (I)

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