Fourier coefficients and slopes of Drinfeld modular forms-Reference-Cited by-同舟云学术

Fourier coefficients and slopes of Drinfeld modular forms

Published:2023-10-04 Issue:10 Volume:19 Page:2523-2553
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Bandini Andrea¹^ORCID,Valentino Maria²

Affiliation:

1. Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

2. Dipartimento di Matematica e Informatica, Università della Calabria, Via P. Bucci Cubo 30B VII piano, 87036 Arcavacata di Rende (CS), Italy

Abstract

Let [Formula: see text] be a Drinfeld modular form of level [Formula: see text] which is an eigenform for the Hecke operator [Formula: see text] ([Formula: see text] a prime of [Formula: see text]). We study the relations between the Fourier coefficients of [Formula: see text] and the [Formula: see text]-adic valuation of its eigenvalue (slope). We use formulas for some of the Fourier coefficients of [Formula: see text] to provide bounds and estimates on the slopes and, in particular, to find necessary conditions for “large” slopes, whose existence is closely connected with conjectures on oldforms and newforms.

Funder

University of Pisa

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042123501245

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