Unimodularity of zeros of period polynomials of Hecke eigenforms

DOI10.1112/blms/bdu007zbMath1311.11027OpenAlexW2123411882MaRDI QIDQ5419239

Wissam Raji, Ahmad El-Guindy

Publication date: 6 June 2014

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/blms/bdu007

zbMATH Keywords

Hecke eigenformsperiod polynomials

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Holomorphic modular forms of integral weight (11F11)

Related Items

Ramanujan’s Formula for ζ(2n + 1), Explorations in the Theory of Partition Zeta Functions, Eichler cohomology and zeros of polynomials associated to derivatives of \(L\)-functions, The ``Riemann hypothesis is true for period polynomials of almost all newforms, Addendum to: Unimodularity of zeros of self-inversive polynomials, On a secant Dirichlet series and Eichler integrals of Eisenstein series, The zeros of odd period polynomials for newforms on \(\Gamma_0 (2)\), The zeros of even period polynomials for newforms on Γ₀(𝑁), Riemann hypothesis for period polynomials of modular forms, 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 for modular form periods, On the zeros of period functions associated to the Eisenstein series for \(\Gamma_0^+(N)\), Zeta-polynomials, Hilbert polynomials, and the Eichler-Shimura identities, Period polynomials, derivatives of \(L\)-functions, and zeros of polynomials, Riemann hypothesis for period polynomials attached to the derivatives of \(L\)-functions of cusp forms for \(\Gamma_0(N)\)

Uses Software

• PARI/GP

Cites Work

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• Real zeros of holomorphic Hecke cusp forms
• Mass equidistribution for Hecke eigenforms
• Periods of modular forms and Jacobi theta functions
• Variations of the Ramanujan polynomials and remarks on \(\zeta(2j+1)/\pi^{2j+1}\)
• Unimodularity of zeros of self-inversive polynomials
• The Nontrivial Zeros of Period Polynomials of Modular Forms Lie on the Unit Circle
• Transcendental values of certain Eichler integrals
• ZEROS OF EISENSTEIN SERIES
• On the Zeros of Eisenstein Series