Bounding periods at supersingular CM points.

The article discusses the construction of a one-variable p-adic L-function for Rankin-Selberg families using the imaginary quadratic field K and the eigenform of weight k. The p-adic L-function is a continuous function on a space of p-adic Hecke characters. Also cited is the use of Theorems 5.48 and 6.21 to allow the p-adic L-function to satisfy an interpolation property equal to central L-values.