Nonvanishing of second coefficients of Hecke polynomials

DOI10.1016/J.JNT.2024.03.014MaRDI QIDQ6556222

Archer Clayton, Hui Xue, Helen Dai, Jake Zummo, Tianyu Ni

Publication date: 17 June 2024

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

Hecke operatorHecke polynomialEichler-Selberg trace formula

Mathematics Subject Classification ID

Holomorphic modular forms of integral weight (11F11) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Hecke-Petersson operators, differential operators (one variable) (11F25)

Cites Work

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• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• The trace of \(T_2\) takes no repeated values
• The vanishing of Ramanujan's function \(\tau(n)\)
• Historical Remark on Ramanujan′s Tau Function
• Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n
• Majorations Explicites Pour le Nombre de Diviseurs de N
• Heights of points on elliptic curves over ℚ
• Vanishing and non-vanishing of traces of Hecke operators
• Répartition asymptotique des valeurs propres de l’opérateur de Hecke 𝑇_𝑝
• The nonvanishing of the trace of \(T_3\)

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