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Showing 1 to 7 of 7 for “"Mock theta functions"”.
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Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook
… letter to G. H. Hardy contains the definition of mock theta functions, a list of 17 mock theta functions, and 5 identities related to mock theta functions. Also, Ramanujan's lost notebook contains many further results on mock theta functions. In particular, the lost notebook contains eight …
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Contributions to Trigonometric Sums and Fifth -Order Mock Theta Functions
… portion of this thesis focuses on Ramanujan's mock theta functions. In the second chapter, we extend the work of G. N. Watson on the fifth order mock theta functions, and show that in comparison to the third order functions, the fifth order mock theta functions possess a more complex behavior …
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Contributions to the Theory of Q-Series and Mock Theta Functions
… imply some of the relations for the third order mock theta functions given by Ramanujan. In Chapter 3, we prove very general theorems on the periodicity of signs of the Taylor series coefficients of a large class of q-products. S. Ramanujan, B. Richmond, G. Szekeres, G. E. Andrews, K. G. …
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Arithmetic of partition functions and q-combinatorics
… modular forms, representation theory, symmetric functions and mathematical physics. Among these, we study the arithmetic of partition functions and q-combinatorics via bijective methods, q-series and modular forms. In particular, regarding arithmetic properties of partition functions, we examine …
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Arithmetic of Maass forms of half-integral weight
… among others. Finally, we focus on the classical mock theta functions of Ramanujan, and give a simple proof of the mock theta conjectures using the modern theory of harmonic Maass forms, especially work of Zwegers and Bringmann-Ono, together with the theory of vector-valued modular forms.
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Modular equations and Ramanujan's cubic and quartic theories of theta functions
… several identities involving Ramanujan's general theta function. In Chapter 2, we give proofs for new Ramanujan type modular equations discovered by Somos and establish applications of some of them. In Chapter 3, we will give proofs for several Dedekind eta product identities which Somos …
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Combinatorial approaches to problems about integer partitions and q-series
… two general q-series identities containing false theta function and mock theta function identities as special cases. Additionally, we introduce a Gaussian coefficient analogue for restricted odd Ferrers diagrams. The second set of objects we study is a class of core partitions. We prove a …