Real zeros of holomorphic Hecke cusp forms

DOI10.4171/JEMS/308zbMath1287.11054arXiv1103.3262OpenAlexW2117575193MaRDI QIDQ409046

Amit Ghosh, Peter C. Sarnak

Publication date: 12 April 2012

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.3262

zbMATH Keywords

real zerosHolomorphic Hecke cusp forms

Mathematics Subject Classification ID

Ordinary differential equations and systems with randomness (34F05) Fourier coefficients of automorphic forms (11F30) Holomorphic modular forms of integral weight (11F11)

Related Items (23)

Multiplicative functions in short intervals ⋮ Real zeros of holomorphic Hecke cusp forms and sieving short intervals ⋮ Nodal domains of Maass forms. I ⋮ The Weyl bound for triple product \(L\)-functions ⋮ Sign changes of fourier coefficients of holomorphic cusp forms at norm form arguments ⋮ Sign changes of Fourier coefficients of Siegel cusp forms of degree two on Hecke congruence subgroups ⋮ ZEROS OF CERTAIN COMBINATIONS OF EISENSTEIN SERIES ⋮ Small‐scale equidistribution of Hecke eigenforms at infinity ⋮ Sign changes of Hecke eigenvalues ⋮ Improved subconvexity bounds for 𝐺𝐿(2)×𝐺𝐿(3) and 𝐺𝐿(3) 𝐿-functions by weighted stationary phase ⋮ On zeros of quasi-modular forms ⋮ Zeros of newform Eisenstein series on \(\Gamma_{0}(N)\) ⋮ Estimates on the zeros of \(E_2\) ⋮ Unimodularity of zeros of period polynomials of Hecke eigenforms ⋮ On the zeros of weakly holomorphic modular forms ⋮ Aperiodicity of signs of Hecke eigenvalues ⋮ Automorphic forms and arithmetic. Abstracts from the workshop held August 30 -- September 5, 2020 (hybrid meeting) ⋮ Zeros of the weight two Eisenstein series ⋮ Zeros of modular forms of half integral weight ⋮ Distinguishing newforms by their Hecke eigenvalues ⋮ Further improvement on bounds for L-functions related to GL(3) ⋮ Cuspidal projections of products of Eisenstein series ⋮ Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mass equidistribution for Hecke eigenforms
• On \(L^{\infty }\) norms of holomorphic cusp forms
• On the zeros and coefficients of certain weakly holomorphic modular forms
• La conjecture de Weil. I
• Uniform bound for Hecke \(L\)-functions
• Gaps between primes, and the pair correlation of zeros of the zeta-function
• On modular signs
• Recent progress on the quantum unique ergodicity conjecture
• On signs of Fourier coefficients of cusp forms
• On zeros of Eisenstein series for genus zero Fuchsian groups
• How many zeros of a random polynomial are real?
• The irreducibility of some level 1 Hecke polynomials
• Almost all short intervals containing prime numbers
• Inequalities for the incomplete gamma function
• THE FIRST NEGATIVE HECKE EIGENVALUE
• On the Zeros of Eisenstein Series

This page was built for publication: Real zeros of holomorphic Hecke cusp forms