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(1995)In the first part of this thesis, we prove Ramanujan's formulas for the coefficients in the power series expansions of certain modular forms. We prove his formulas for the coefficients of 1/$E\sb4, E\sb4/E\sb6$ and other ...
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Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and Lfunctions (20150803)The focus of the first part of the thesis commences with an examination of two pages in Ramanujan's lost notebook, pages 336 and 335. A casual, or even more prolonged, examination of the strange formulas on these pages ...
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(20150121)In this dissertation, we study three problems about Ramsey theory. First, we prove a selfdual Ramsey theorem for parameter systems which is a generalization of the selfdual Ramsey theorem developed by Solecki. Second, ...
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(2000)Given an adapted probability measure on a locally compact group, there are a variety of support conditions which cause the concentration functions to go to zero. This work discusses the rate of this decay under many such ...
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(2003)Finally, this thesis uses dynamical systems techniques to prove already known results in continued fractions.
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(2008)Lattice varieties play an important role in several areas of mathematics. In this thesis we investigate the properties of rational points on lattice varieties over Witt vectors with algebraically closed residue field in ...
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(1992)Let F$\sb{n,m}$ denote the set of all real forms of degree m in n variables. In 1888, Hilbert proved that a form P $\in$ F$\sb{n,m}$ which is positive semidefinite (psd) must have a representation as a sum of squares (sos) ...
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(2000)Although the 'Inductive' form of Dade's conjecture must be verified for all finite, nonabelian, simple groups G, for most such G it suffices to verify a simpler form of the conjecture. In this thesis we will introduce ...
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(20170705)Suppose $f(x,y)$ is a binary form of degree $d$ with coefficients in a field $K \subseteq \cc$. The {\it $K$rank of $f$} is the smallest number of $d$th powers of linear forms over $K$ of which $f$ is a $K$linear ...
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(20120918)This thesis builds on the recently begun extension of continuum thermomechanics to fractal media which are specified by a fractional mass scaling law of the resolution length scale R. The focus is on prefractal media ...
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Now showing items 866885 of 1135