Browse Dissertations and Theses - Mathematics by Contributor "Ahlgren, Scott"

  • Andersen, Nickolas Robert (2016-06-15)
    We investigate the arithmetic properties of coefficients of Maass forms in three contexts. First, we discuss connections to invariants of real and imaginary quadratic fields, expanding on the work of Zagier and Duke-Imamoglu-Toth. ...

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  • Kim, Byung Chan (2010-05-14)
    Integer partitions play important 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 ...

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  • Kilbourn, Timothy (2007)
    Fourier coefficients of modular forms have profound connections with many areas of number theory. We will consider three different applications of these coefficients. First, we extend the Apery number supercongruence, ...

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  • Treneer, Stephanie (2006)
    Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. In each case, the values of the given arithmetic function appear as the Fourier ...

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  • Dewar, Michael P. (2010-05-19)
    We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the ...

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  • Skabelund, Dane C. (2018-04-20)
    This thesis is comprised of three parts, each dealing with one or more of the Hermitian, Suzuki, and Ree curves, which are three families of algebraic curves over finite fields which have pronounced arithmetic and geometric ...

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  • Schultz, Daniel (2014-09-16)
    This thesis is centered 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 ...

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  • Koukoulopoulos, Dimitrios (2010-08-20)
    In 1955 Erdõs posed the multiplication table problem: Given a large integer N, how many distinct products of the form ab with a≤N and b≤N are there? The order of magnitude of the above quantity was determined by Ford. The ...

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  • Jeon, Bo Gwang (2013-08-22)
    For a single cusped hyperbolic 3-manifold, Hodgson proved that there are only finitely many Dehn fillings of it whose trace fields have bounded degree. In this paper, we conjecture the same for manifolds with more cusps, ...

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  • Xu, Ping (2013-08-22)
    My dissertation 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 ...

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  • Gugg, Chadwick (2011-01-21)
    In his notebooks, Ramanujan recorded 40 beautiful modular relations for the Rogers-Ramanujan functions. Of these 40 identities, precisely one involves powers of the Rogers-Ramanujan functions. Ramanujan added the enigmatic ...

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  • Sinick, Jonah D. (2011-08-25)
    In the first part of this thesis we generalize a theorem of Kiming and Olsson concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions ...

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  • Prugsapitak, Supawadee (2009)
    In this dissertation, we study the Tarry-Escott problem and some related diophantine systems over Z and over some quadratic fields. We give infinitely many solutions of the Tarry-Escott problem over Zi of degrees 2, ...

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