Browse Graduate Dissertations and Theses at Illinois by Subject "q-series"
Now showing items 1-4 of 4
(2010-05-14)Integer partitions play important roles in diverse areas of mathematics such as q-series, the theory of modular forms, representation theory, symmetric functions and mathematical physics. Among these, we study the arithmetic ...
(2020-07-06)In this thesis, we study three types of partition-theoretic objects. The first objects studied are odd Ferrers diagrams, which we use in new combinatorial proofs of two general q-series identities containing false theta ...
(2015-01-21)Some of the most interesting of Ramanujan's continued fraction identities are those involving ratios of Gamma functions in Chapter 12 of his second notebook. This thesis develops a method for deriving such identities, ...
(2011-01-21)In his notebooks, Ramanujan recorded 40 beautiful modular relations for the Rogers-Ramanujan functions. Of these 40 identities, precisely one involves powers of the Rogers-Ramanujan functions. Ramanujan added the enigmatic ...