Alladi Ramakrishnan Hall

Strong multiplicity one in the context of $l$-adic Galois representations

C. S. Rajan

TIFR

We discuss an algebraic Chebotarev density theorem.
We deduce that if two non-CM cuspforms have equal Hecke
eigenvalues at a set of places positive density, then the forms are twists
of each other by a Dirichlet character. We also consider the question of
potential equivalence in the context of Galois representations: whether
two representations which are locally potentially equivalent are globally
potentially equivalent, and discuss the solution for two dimensions.