Date of Award
Master of Science (MS)
Dr. Timothy Huber
Dr. Brandt Kronholm
Dr. Jacob White
MacMahon provided Ramanujan and Hardy a table of values for p(n) with the partitions of the first 200 integers. In order to make the table readable, MacMahon grouped the entries in blocks of five. Ramanujan noticed that the last entry in each block was a multiple of 5. This motivated Ramanujan to make the following conjectures, p(5n+4) ≡ 0 (mod 5); p(7 n+5) ≡ 0 (mod 7); p(11n+6) ≡ 0 (mod 11) which he eventually proved.
The purpose of this thesis is to give new proofs for Ramanujan's partition congruences. This would be done by using theta functions to construct certain vector spaces of modular forms. Computations within these vector spaces result in new proofs for Ramanujan's partition congruences modulo five and seven. Similar techniques will use to derive congruences for a wider class of generating functions.
Huerta, Mayra C., "A New Approach to Ramanujan's Partition Congruences" (2017). Theses and Dissertations - UTRGV. 118.