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A higher weight analogue of Ogg’s theorem on Weierstrass points
- Source :
- International Journal of Number Theory. 17:1155-1162
- Publication Year :
- 2020
- Publisher :
- World Scientific Pub Co Pte Lt, 2020.
-
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.
- Subjects :
- Algebra and Number Theory
Computer Science::Information Retrieval
Modular form
Astrophysics::Instrumentation and Methods for Astrophysics
Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)
Cusp form
Modular curve
Combinatorics
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
Integer
Genus (mathematics)
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
ComputingMethodologies_DOCUMENTANDTEXTPROCESSING
Weierstrass point
Computer Science::General Literature
Order (group theory)
ComputingMilieux_MISCELLANEOUS
Mathematics
Subjects
Details
- ISSN :
- 17937310 and 17930421
- Volume :
- 17
- Database :
- OpenAIRE
- Journal :
- International Journal of Number Theory
- Accession number :
- edsair.doi...........8f08b8d520f198dc2a156d7a302d08fb