Computing Euler products and coefficients of classical modular forms for twisted L-functions

2025/07/09 by Pascal Molin, Molin, Pascal
Computer Science · Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.2507.06681

openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe a complete algorithm to compute millions of coefficients of classical modular forms in a few seconds. We also review operations on Euler products and illustrate our methods with a computation of triple product L-function of large conductor.

Citations

• Modular Forms in Pari/GP
• A computation of modular forms of weight one and small level
• Computing modular Galois representations
• Toric modular forms of higher weight
• Approximate formulas for some functions of prime numbers

Related

• Testing the functional equations of a high-degree Euler product
• Bounds for Moments of Twisted Fourier coefficients of Modular Forms
• Bilinear forms with Kloosterman sums and moments of twisted L-functions
• Twisted Hilbert modular L-functions and spectral theory
• Formulas for central critical values of twisted L-functions attached to paramodular forms