Browse Dissertations and Theses - Mathematics by Contributor "Ford, Kevin"

  • 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, Sun (2010-05-14)
    This dissertation involves two topics. The first is on the theory of partitions, which is discussed in Chapters 2 − 5. The second is on covering systems, which are considered in Chapters 6 − 8. In 2000, Farkas and Kra ...

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  • Vandehey, Joseph (2013-05-24)
    We improve the error term in the van der Corput transform for exponential sums, \sum g(n) exp(2 \pi i f(n)). For many smooth functions g and f, we can show that the largest factor of the error term is given by a simple ...

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  • Li, Junxian (2018-06-01)
    The value distribution of the Riemann zeta function $\zeta(s)$ is a classical question. Despite the fact that values of $\zeta(s)$ are approximately Gaussian distributed, $\zeta(s)$ can be very large for infinitely many ...

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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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  • 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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  • Dong, Dong (2018-06-22)
    We first give a survey on multilinear Hilbert transforms. Then we study several variants of bilinear Hilbert transform such as bilinear Hilbert transform along two polynomials, discrete (integer) bilinear Hilbert transform ...

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  • Malik, Amita (2017-07-13)
    PART I G. H. Hardy and S. Ramanujan established an asymptotic formula for the number of unrestricted partitions of a positive integer, and claimed a similar asymptotic formula for the number of partitions into perfect ...

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  • Meng, Xianchang (2017-07-07)
    This thesis includes four chapters. In Chapter 1, we briefly introduce the history and the main results of the topics of this thesis: the distribution of $k$-free numbers and the derivative of the Riemann zeta-function, ...

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  • Shakan, George (2019-02-19)
    The sum-product problem of Erdos and Szemeredi asserts that any subset of the integers has many products or many sums. We explore quantitative aspects of the problem over both the real numbers and finite fields of prime order.

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  • Pratt, Kyle (2019-04-12)
    We investigate properties of prime numbers and L-functions, and interactions between these two topics. First, we discuss the problem of primes in thin sequences, expanding on work of Maynard and Friedlander-Iwaniec. Next, ...

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