Linnik problem for Maass-Hecke cusp forms and effective multiplicity one theorem

Abstract: The strong multiplicity one theorem (for GL(2), proved by Jacquet and Langlands) implies that if two Maass-Hecke cuspforms share the same Laplacian eigenvalue and the same Hecke eigenvalues for almost all primes then the two forms must be equal up to a constant multiple. In this talk we consider the following question, an analogue of Linnik’s question for Dirichlet characters: if the two forms are not equal up to a constant multiple, how large can the first prime p be, such that the corresponding Hecke eigenvalues differ? Alternatively we can also ask: how large is the dimension of the joint eigenspace of the given finite set of Hecke operators and the Laplace operator? We approach these two questions with two different methods. This is a joint work with Junehyuk Jung.

number theory

Audience: researchers in the topic

London number theory seminar

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