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An Analysis Of Antichimeral Ramanujan Type Congruences For Quotients Of The Rogers-Ramanujan Functions, Ryan A. Mowers
An Analysis Of Antichimeral Ramanujan Type Congruences For Quotients Of The Rogers-Ramanujan Functions, Ryan A. Mowers
Theses and Dissertations
This paper proves the existence of antichimeral Ramanujan type congruences for certain modular forms These modular forms can be represented in terms of Klein forms and the Dedekind eta function. The main focus of this thesis is to introduce the necessary theory to characterize these specific Ramanujan type congruences and prove their antichimerality.
Congruences For Quotients Of Rogers-Ramanujan Functions, Maria Del Rosario Valencia Arevalo
Congruences For Quotients Of Rogers-Ramanujan Functions, Maria Del Rosario Valencia Arevalo
Theses and Dissertations
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.