#### 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.

Done