Work

Determination of a pair of newforms from the product of their twisted central values

Year: 2024

Type: article

Abstract: We show that a pair of newforms ( f , g ) (f,g) can be uniquely determined by the product of the central 𝐿-values of their twists. To achieve our goal, we prove an asymptotic formula for the average of the product of the central values of two twisted 𝐿-functions, L ⁢ ( 1 / 2 , f × χ ) ⁢ L ⁢ ( 1 / 2 , g × χ ⁢ ψ ) L(1/2,f\times\chi)L(1/2,g\times\chi\psi) , where ( f , g ) (f,g) is a pair of newforms. The average is taken over the primitive Dirichlet characters 𝜒 and 𝜓 of distinct prime moduli.

Source: Forum Mathematicum

DOI: 10.1515/forum-2023-0373

Authors: Pramath Anamby, Ritwik Pal

Institutions: Indian Institute of Science Education and Research Pune, Indian Statistical Institute

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Board for Higher Mathematics

Awards: G3585507992, G6719832478