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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

3-adic Properties of Hecke Traces of Singular Moduli

Beazer, Miriam 19 July 2021 (has links)
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.

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