2023/01/02 by Robin Zhang, Zhang, Robin · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research
paper · pdf · doi:10.48550/arxiv.2301.00612
The first two papers in this series prove the Harris-Venkatesh conjecture and its refinement with the Stark conjecture for imaginary dihedral modular forms of weight 1. This paper explicitly describes the constants appearing in the Harris-Venkatesh (plus Stark) conjecture for dihedral modular forms by evaluating GL(2) × GL(2) Rankin--Selberg periods and zeta integrals on newforms and optimal forms. One consequence is a formula for the ratio between Petersson norms and adjoint L-values. Our calculations also extend to exotic modular forms whose level is odd or whose Deligne-Serre representation is 2-ordinary.