Abstract
Let F be a number field, fan algebraic automorphic newform on GL(2) over F, pan odd prime does not divide the class number of F and the level off. We prove that f is determined by its L-values twisted by Galois characters phi of certain Zp-extension of F. Furthermore, if F is totally real or CM, then under some mild assumption on f, the compositum of the Hecke field off and the cyclotomic field Q(phi) is generated by the algebraic L-values of f twisted by Galois characters phi of certain Zp-extension of F. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

https://doi.org/10.1016/j.jnt.2025.02.006