Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
Results
Showing 1 to 16 of 16 for “"Q-series"”.
-
Knots, Skein Theory and q-Series
The tail of a sequence {P_n(q)} of formal power series in Z[q^{-1}][[q]], if it exists, is the formal power series whose first $n$ coefficients agree up to a common sign with the first n coefficients of P_n. The colored Jones polynomial is link invariant that associates to every link in S^3 a …
-
Q-Continued Fractions and Related Q-Series
In Chapter 5, we prove two other equations on page 45 of Ramanujan's lost notebook by using the Bauer-Muir transformation and by using the method of successive approximation. Also, we prove several continued fractions of Ramanujan which are related to the odd parts of continued fractions.
-
Combinatorial approaches to problems about integer partitions and q-series
… use in new combinatorial proofs of 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 …
-
Contributions to the Theory of Q-Series and Mock Theta Functions
In Chapter 2, we prove, for the first time, a series of four related identities from Ramanujan's lost notebook. These are one-parameter identities which would directly imply some of the relations for the third order mock theta functions given by Ramanujan. In Chapter 3, we prove very general …
-
Infinite Series Identities in the Theory of Elliptic Functions and Q-Series
We prove several infinite series identities. In Chapter 2, We extend C. L. Siegel's method of proving the Dedekind-eta function transformation by integrating some selected functions over a positively oriented polygon, generalizing Siegel's integration over a parallelogram. As consequences, we …
-
Arithmetic of partition functions and q-combinatorics
… 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 of partition functions and q-combinatorics via bijective methods, q-series and modular forms. In …
-
Investigations Into Cranks of Partitions, Trigonometric Sums, and Q-Integrals
… evaluations follow from well-known product-series identities from the theory of q-series.
-
Product Identities for Theta Functions
… we derive a general method for establishing q-series identities. Using this method, we can show that if Zn can be taken as the disjoint union of a lattice generated by n linearly independent vectors in Z n and a finite number of its translates, certain products of theta functions can be written …
-
Rademacher-Type Series
Unavailable
-
An analytical and experimental investigation of a frequency- shift-keyed signal generated by a phase-locked-loop with application to narrowband FSK
… networks excited by the FS-PLL, an infinite series of damped sinusoidal terms, representing the PLL output signal is developed. This series is also utilized to determine the coefficients of the Fourier series representation of a periodically keyed PLL. Using this result, the signal bandwidth …
-
Bijective proofs of partition identities and covering systems
… in the theory of theta functions and q-series, and dates back to 1916 or earlier. In his recent survey paper on this identity, Shaun Cooper remarked that there does not exist a bijective proof of it. In Chapter 3, employing bijective proofs of Jacobi’s triple product identity and Euler’s …
-
Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues
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, using hypergeometric functions as the main tool. We begin by deriving a continued …
-
Modular identities for the Rogers-Ramanujan functions and analogues
Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2011-01-21T22:47:37Z Item is restricted until 2013-01-21T22:47:37Z
-
Transformation formulas associated with integrals involving the Riemann Ξ-function and rank-crank type PDEs in partition theory
… through certain bilateral basic hypergeometric series identities due to M.~Jackson and S.H.~Chan. The motivation comes from the fact that the original Rank-Crank PDE due to A.O.L.~Atkin and F.G.~Garvan was obtained through an identity of Atkin and H.P.F.~Swinnerton-Dyer, which is a special case …