Two-variable p-adic L-functions of modular forms for non-ordinary primes

Text. For a prime p which is non-ordinary for a given eigenform f(z), we construct a non-integral two-variable p-adic L-function that interpolates the Rankin convolutions of an eigenform f(z) and the theta series of Hecke characters of an imaginary quadratic field K. Our work is a non-ordinary analogue of Hida's two-variable p-adic L-functions for ordinary primes p. (C) 2014 Elsevier Inc. All rights reserved.