Abstract

As shown by Zagier, singular moduli can be represented by the coefficients of a certain half integer weight modular form. Congruences for singular moduli modulo arbitrary primes have been proved by Ahlgren and Ono, Edixhoven, and Jenkins. Computation suggests that stronger congruences hold for small primes $p \in \{2, 3, 5, 7, 11\}$. Boylan proved stronger congruences hold in the case where $p=2$. We conjecture congruences for singular moduli modulo powers of $p \in \{3, 5, 7, 11\}$. In particular, we study the case where $p=3$ and reduce the conjecture to a congruence for a simpler modular form.

Degree

MS

College and Department

Physical and Mathematical Sciences

Rights

https://lib.byu.edu/about/copyright/

Date Submitted

2021-07-19

Document Type

Thesis

Handle

http://hdl.lib.byu.edu/1877/etd11831

Keywords

modular forms, congruences, singular moduli

Language

english

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