P-adic Rankin-Selberg L-functions in universal deformation families and functional equations

Abstract

We construct a $p$-adic Rankin-Selberg $L$-function associated to the product of two families of modular forms, where the first is an ordinary (Hida) family, and the second an arbitrary universal-deformation family (without any ordinarity condition at $p$). This gives a function on a 4-dimensional base space - strictly larger than the ordinary eigenvariety, which is 3-dimensional in this case. We prove our $p$-adic $L$-function interpolates all critical values of the Rankin-Selberg $L$-functions for the classical specialisations of our family, and derive a functional equation for our $p$-adic $L$-function.

arXiv commentBased on the first author's University of Warwick PhD thesis. Revised version, 22 pages

References in corpus (6)

• Variation of Iwasawa invariants in Hida families
• Rankin--Eisenstein classes and explicit reciprocity laws
• Euler systems for Rankin--Selberg convolutions of modular forms
• Rankin--Eisenstein classes in Coleman families
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• Iwasawa Invariants for Symmetric Square Representations