Zeta-polynomials for modular form periods

DOI10.1016/j.aim.2016.10.004zbMath1392.11023arXiv1602.00752OpenAlexW2962823467MaRDI QIDQ728224

D. Kharzeev

Publication date: 19 December 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.00752

zbMATH Keywords

Stirling numbersmodular formsBloch-Kato conjectureEhrhart polynomialsTamagawa numberzeta-polynomials

Mathematics Subject Classification ID

Bell and Stirling numbers (11B73) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11) Galois cohomology (11R34)

Related Items (7)

Explorations in the Theory of Partition Zeta Functions ⋮ Eichler cohomology and zeros of polynomials associated to derivatives of \(L\)-functions ⋮ Homotopy types and geometries below Spec(ℤ) ⋮ The Riemann hypothesis for period polynomials of Hilbert modular forms ⋮ Special values of motivic \(L\)-functions and zeta-polynomials for symmetric powers of elliptic curves ⋮ Zeta-polynomials, Hilbert polynomials, and the Eichler-Shimura identities ⋮ Period polynomials, derivatives of \(L\)-functions, and zeros of polynomials

Cites Work

• Periods of modular forms and Jacobi theta functions
• Motives for modular forms
• Notes on the roots of Ehrhart polynomials
• Periods of modular forms on \(\Gamma_0(N)\) and products of Jacobi theta functions
• Lattice polytopes, Hecke operators, and the Ehrhart polynomial
• Norm bounds for Ehrhart polynomial roots
• Local zeta factors and geometries under SpecZ
• Modular forms and period polynomials
• The Nontrivial Zeros of Period Polynomials of Modular Forms Lie on the Unit Circle
• Riemann hypothesis for period polynomials of modular forms
• On the zeros of certain polynomials
• Unimodularity of zeros of period polynomials of Hecke eigenforms
• Congruences of modular forms and Selmer groups
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