A higher weight analogue of Ogg’s theorem on Weierstrass points-Reference-Cited by-同舟云学术

A higher weight analogue of Ogg’s theorem on Weierstrass points

Published:2020-10-23 Issue:05 Volume:17 Page:1155-1162
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Dicks Robert¹^ORCID

Affiliation:

1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street Urbana, Illinois 61801, USA

Abstract

For a positive integer [Formula: see text], we say that [Formula: see text] is a Weierstrass point on the modular curve [Formula: see text] if there is a non-zero cusp form of weight [Formula: see text] on [Formula: see text] which vanishes at [Formula: see text] to order greater than the genus of [Formula: see text]. If [Formula: see text] is a prime with [Formula: see text], Ogg proved that [Formula: see text] is not a Weierstrass point on [Formula: see text] if the genus of [Formula: see text] is [Formula: see text]. We prove a similar result for even weights [Formula: see text]. We also study the space of weight [Formula: see text] cusp forms on [Formula: see text] vanishing to order greater than the dimension.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042121500299

Reference8 articles.

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