Real zeros of holomorphic Hecke cusp forms

Abstract

This note is concerned with the zeros of holomorphic Hecke cusp forms of large weight on the modular surface. The zeros of such forms are symmetric about three geodesic segments and we call those zeros that lie on these segments, real. Our main results give estimates for the number of real zeros as the weight goes to infinity.

References in corpus (1)

• On the asymptotic distribution of zeros of modular forms

Cited by in corpus (17)

• Nodal domains of Maass forms I
• Improved subconvexity bounds for GL(2)xGL(3) and GL(3) L-functions by weighted stationary phase
• Zeros of certain combinations of Eisenstein series
• The Weyl bound for triple product L-functions
• Nodal domains of Maass forms II
• Zeros of the weight two Eisenstein Series
• Sign changes of Fourier coefficients of Siegel cusp forms of degree two on Hecke congruence subgroups
• Sign changes of Hecke eigenvalues
• Zeros of weakly holomorphic modular forms of levels 2 and 3
• On the zeros of weakly holomorphic modular forms
• Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms
• An explicit bound for the first sign change of the Fourier coefficients
• The Liouville function in short intervals [after Matomaki and Radziwill]
• Monotone chains of Fourier coefficients of Hecke cusp forms
• Zeros of weakly holomorphic modular forms of level 4
• Quantum variance for holomorphic Hecke cusp forms on the vertical geodesic
• Zeros of modular forms of half integral weight