Lifting of vector-valued automorphic forms

TL;DR

This paper investigates the lifting process of logarithmic vector-valued automorphic forms, providing explicit calculations of their Fourier coefficients, thereby advancing understanding of their structure and transformations.

Contribution

It extends previous work by explicitly analyzing lifts for logarithmic vector-valued automorphic forms and computing their Fourier coefficients.

Findings

Explicit Fourier coefficients for lifted forms derived

Lifting properties for logarithmic vector-valued automorphic forms established

Enhanced understanding of automorphic form transformations

Abstract

Recently, the first author [1] showed that the admissible vector-valued automorphic forms lift to the admissible ones. In this article, we study the lifts for the logarithmic vector-valued automorphic forms and explicitly compute the Fourier coefficients of the lifted vector-valued automorphic forms.