Bounds on the multiplicity of the Hecke eigenvalues

2018/10/04 by Naser T. Sardari, Sardari, Naser T.
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1810.02014

Abstract

Fix an integer N and a prime p\nmid N where p≥ 5. We show that the number of newforms f (up to a scalar multiple) of level N and even weight k such that T_p(f)=0 is bounded independently of k, where T_p(f) is the Hecke operator.

Related

• The number of Hecke eigenvalues of same signs
• Vanishing Fourier Coefficients of Hecke Eigenforms
• The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms
• Comparing Hecke eigenvalues of newforms
• Traces of Hecke operators on Drinfeld modular forms for \mathbbF_q[T]