2006/01/07 by David W. Farmer, Farmer, David W., Sarah Zubairy +1
Mathematics · #11F66 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.math/0601143
openalex publication_date 2006/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is believed that Dirichlet series with a functional equation and Euler product of a particular form are associated to holomorphic newforms on a Hecke congruence group. We perform computer algebra experiments which find that in certain cases one can associate a kind of ``higher order modular form'' to such Dirichlet series. This suggests a possible approach to a proof of the conjecture.