NON-COMMUTATIVE p-ADIC L-FUNCTIONS FOR SUPERSINGULAR PRIMES

Abstract

Let E/ℚ be an elliptic curve with good supersingular reduction at p with a p (E) = 0. We give a conjecture on the existence of analytic plus and minus p-adic L-functions of E over the ℤ p -cyclotomic extension of a finite Galois extension of ℚ where p is unramified. Under some technical conditions, we adopt the method of Bouganis and Venjakob for p-ordinary CM elliptic curves to construct such functions for a particular non-abelian extension.