Congruences for Quotients of Rogers-Ramanujan Functions

Author

Maria Del Rosario Valencia Arevalo, The University of Texas Rio Grande Valley

Date of Award

5-2023

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Timothy Huber

Second Advisor

Dr. Brandt Kronholm

Third Advisor

Dr. Elena Polateva

Abstract

In 1919 the mathematician Srinivasa Ramanujan conjectured congruences for the partition function p(n) modulo powers of the primes 5,7,11. In this work, we study Ramanujan type congruences modulo powers of primes p = 7,11,13,17,19,23 satisfied by the Fourier coefficients of quotients the Rogers-Ramanujan Functions G(τ) and H(τ) and the Dedekind eta function η(5τ). In addition to deriving new congruences, we develop the foundational theory of modular forms to motivate and prove the results. The work includes proofs of congruences facilitated by Python/SageMath code.

Comments

Copyright 2023 Maria del Rosario Valencia Arevalo. All Rights Reserved.

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Recommended Citation

Valencia Arevalo, M. D. (2023). Congruences for Quotients of Rogers-Ramanujan Functions [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/1265