Riemann hypothesis for period polynomials of modular forms

DOI10.1073/pnas.1600569113zbMath1412.11075arXiv1601.03114OpenAlexW2237579816WikidataQ36684672 ScholiaQ36684672MaRDI QIDQ2962319

Ken Ono, Seokho Jin, Wenjun Ma, Kannan Soundararajan

Publication date: 16 February 2017

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.03114

zbMATH Keywords

period polynomialsBirch and Swinnerton-Dyermodular \(L\)-functions

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) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (17)

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 ⋮ The zeros of odd period polynomials for newforms on \(\Gamma_0 (2)\) ⋮ The zeros of even period polynomials for newforms on Γ₀(𝑁) ⋮ Linear independence of even periods of modular forms ⋮ 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 for modular form periods ⋮ Ramanujan identities of higher degree ⋮ 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 ⋮ An algebraic characterization of the Kronecker function ⋮ Riemann hypothesis for period polynomials attached to the derivatives of \(L\)-functions of cusp forms for \(\Gamma_0(N)\)

Cites Work

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• A property of L-functions on the real line
• Periods of modular forms and Jacobi theta functions
• Newforms and functional equations
• La conjecture de Weil. I
• Hecke operators on \(\Gamma_0(m)\)
• Modular forms and period polynomials
• The Nontrivial Zeros of Period Polynomials of Modular Forms Lie on the Unit Circle
• Transcendental values of certain Eichler integrals
• Some new results on the Eichler cohomology of automorphic forms
• Unimodularity of zeros of period polynomials of Hecke eigenforms

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