A study on q-series and partitions
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Date
2025
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Department of Mathematics, NITS
Abstract
This Thesis explores the rich field of the q-series, highlighting how it interacts with three important mathematical theorems: Euler’s identity, the Jacobi triple product and the Pentagonal number Theorem, Ramnujan’s Partition Congruences. A foundation for comprehending the structure of q-series and their generating functions is provided by Euler’s identity. The depth of q-series is further demonstrated by the Pentagonal Number Theorem, which relates to combinatorics and integer partitions. Together, these results illustrate the profound coherence of the q− series within mathematics.