On mod $p^c$ transfer and applications

TL;DR

This paper develops a mod p^c transfer concept for automorphic forms, enabling the construction of p-adic families of Siegel eigenforms through trace formula comparisons and congruence analysis.

Contribution

It introduces a mod p^c transfer framework for automorphic forms, extending classical transfer ideas to congruences and p-adic families.

Findings

Established mod p^c transfer via trace formula comparison

Constructed finite slope p-adic families of Siegel eigenforms

Analyzed properties of mod p^c reduced multiplicities

Abstract

We study a mod $p^c$ analog of the notion of transfer for automorphic forms. Instead of existence of eigenforms, such transfers yield congruences between eigenforms but, like transfers, we show that they can be established by a comparison of trace formulas. This rests on the properties of mod $p^c$ reduced multiplicities which count congruences between eigenforms. As an application we construct finite slope $p$-adic {\it continuous} families of Siegel eigenforms using a comparison of trace formulas.