On certain constructions of p-adic families of Siegel modular forms of even genus

TL;DR

This paper constructs p-adic analytic families of Siegel cusp forms of even genus from Hida's elliptic forms using the Duke-Imamoglu lifting, extending p-adic families to higher genus cases.

Contribution

It introduces a method to build p-adic families of Siegel modular forms of arbitrary even genus from elliptic forms, expanding the scope of p-adic modular form theory.

Findings

Constructed p-adic families of Siegel cusp forms of even genus.

Extended Hida's elliptic form families to higher genus via Duke-Imamoglu lifting.

Provided results for Siegel Eisenstein series with trivial Nebentypus.

Abstract

Suppose that p > 5 is a rational prime. Starting from a well-known p-adic analytic family of ordinary elliptic cusp forms of level p due to Hida, we construct a certain p-adic analytic family of holomorphic Siegel cusp forms of arbitrary even genus and of level p associated with Hida's p-adic analytic family via the Duke-Imamoglu lifting which has been established by Ikeda. Moreover, we also give a similar results for the Siegel Eisenstein series of even genus with trivial Nebentypus.