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 20 of 25 for “"theta functions"”.
-
Identities involving theta functions and analogues of theta functions
… is mainly about various identities involving theta functions and analogues of theta functions. In Chapter 1, we give a completely elementary proof of Ramanujan's circular summation formula of theta functions and its generalizations given by S. H. Chan and Z. -G. Liu, and J. M. Zhu, who used …
-
Product Identities for Theta Functions
… number of its translates, certain products of theta functions can be written as linear combinations of other products of theta functions. Many known identities, including M. D. Hirschhorn's generalization of the quintuple product identity, several modular relations for the Gollnitz-Gordon …
-
Analytic representations of quantum systems with Theta functions
… in a cell S in the complex plane using Theta functions, is defined. The analytic functions have exactly d zeros in a cell S. The reproducing kernel plays a central role in this formalism. Wigner and Weyl functions are also studied. Quantum systems with positions in a circle S and momenta …
-
Theorems on Theta Functions in Ramanujan's Lost Notebook
Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs
-
Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook
… 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 identities …
-
Transformations of Theta-Functions and Analogues of Dedekind Sums
… formulae for the logarithms of the classical theta-functions. These sums, which we refer to as Berndt sums, are analogous to Dedekind sums, which arise in a similar manner from the transformation formula for the logarithm of the Dedekind eta-function. In this thesis, we deduce a number of …
-
Cubic theta functions and identities for Appell's F1 function
… around three topics: the theory of the cubic theta functions as functions of two analytic variables, cubic modular equations, and a class of two-variable cubic modular equations. Chapter 2 is dedicated to the rst two topics, while Chapter 3 covers the last. First, the theory of cubic theta …
-
Contributions to Trigonometric Sums and Fifth -Order Mock Theta Functions
… 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 on …
-
Contributions to the Theory of Q-Series and Mock Theta Functions
… 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. Ramanathan, …
-
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 …
-
Theta functions and division points on Abelian varieties of dimension two
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1985.
-
An Arithmetic-geometric Reciprocity between Theta Functions Attached to Real and Imaginary Quadratic Fields
We use the theta correspondence to construct classical holomorphic modular forms associated to ideal classes in quadratic number fields. These modular forms are theta functions that were originally introduced by Hecke in the 1920s andhave been investigated by several authors since. Our framework …
-
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 …
-
Arithmetic of Maass forms of half-integral weight
… 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.
-
The blowup formula for higher rank Donaldson invariants
… function completely, and show that it is a theta function on a family of genus 2 hyperelliptic Jacobians. Finally, I give a formal argument to explain the appearance of Abelian varieties and theta functions in four dimensional topological field theories.
-
Development of unsaturated flow functions for low impact development stormwater management systems filter media and flow routines for hydrological modeling of permeable pavement systems
… for over a year and it was found that the system functions under unsaturated conditions. Saturation was never observed at any levels in the system over the period of study. Solving Richards' Equation, which is typically used to represent flow in unsaturated soils, requires knowledge of the …
-
F-virtual Abelian Varieties and Rallis Inner Product Formula
… groups. With this we can compute the pairing of theta functions and show in this case that it is related to the central value of Langlands L-function. This new case of Rallis inner product formula enables us to relate nonvanishing of L-value to the nonvanishing of theta lifting.
-
An analytic representation of weak mutually unbiased bases
… representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three apparently different …
-
Analogues of Dedekind Sums
… C. Berndt did analogous work with the classical theta-functions and introduced the sum$$S(d, c) = \sum\sbsp{j=1}{c-1}({-}1)\sp{j+1+\lbrack dj/c\rbrack},$$among others. There is considerable literature on the Dedekind sum and its generalizations. This thesis develops the arithmetic theory of the …
Page 1 of 2