Congruences for coefficients of modular functions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-12

AUTHORS

Paul Jenkins, D. J. Thornton

ABSTRACT

We examine canonical bases for weakly holomorphic modular forms of weight 0 and level p=2,3,5,7,13 with poles only at the cusp at ∞. We show that many of the Fourier coefficients for elements of these canonical bases are divisible by high powers of p, extending results of the first author and Andersen. Additionally, we prove similar congruences for elements of a canonical basis for the space of modular functions of level 4, and give congruences modulo arbitrary primes for coefficients of such modular functions in levels 1, 2, 3, 4, 5, 7, and 13. More... »

PAGES

619-628

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11139-014-9628-x

DOI

http://dx.doi.org/10.1007/s11139-014-9628-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1013843724


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