Non-vanishing of class group L-functions for number fields with a small regulator

DOI10.1112/S0010437X20007472zbMath1473.11210arXiv1901.06710OpenAlexW3113063321MaRDI QIDQ5148397

Ilya Khayutin

Publication date: 4 February 2021

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.06710

zbMATH Keywords

equidistributionclass groupPhragmén-Lindelöf principlenon-vanishingEpstein zeta functionescape of mass\(L\) functionperidic torus orbitvolume unit ball

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Other Dirichlet series and zeta functions (11M41) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66) Real zeros of (L(s, chi)); results on (L(1, chi)) (11M20) Zeta functions and (L)-functions of number fields (11R42) Algebraic numbers; rings of algebraic integers (11R04)

Related Items

Wide moments of L-functions. I: Twists by class group characters of imaginary quadratic fields

Cites Work

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• Weak subconvexity for central values of \(L\)-functions
• Distribution of periodic torus orbits and Duke's theorem for cubic fields
• On the Phragmén-Lindelöf theorem and some applications
• Distribution of periodic torus orbits on homogeneous spaces
• Séries d'Eisenstein, intégrales toroïdales et une formule de Hecke. (Eisenstein series, toroidal integrals and a formula of Hecke)
• The minima of quadratic forms and the behavior of Epstein and Dedekind zeta functions
• The subconvexity problem for Artin \(L\)-functions
• Non-vanishing of class group \(L\)-functions at the central point.
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• On Selberg's eigenvalue conjecture
• Artin-root numbers and normal integral bases for quaternion fields
• Families of L-Functions and Their Symmetry
• On a question of Lehmer and the number of irreducible factors of a polynomial
• Algebraic integers whose conjugates lie near the unit circle
• Bessel Series Expansions of the Epstein Zeta Function and the Functional Equation
• SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN -FUNCTIONS
• Zeros of Dirichlet $L$-functions
• Bounds for modular L-functions in the level aspect☆
• Algebraic integers near the unit circle
• On Character Sums and L -Series. II
• The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros