# Dept. of Mathematics

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• (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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• (2018-07-19)
Solving Satisfiability Modulo Theories (SMT) problems in a key piece in automating tedious mathematical proofs. It involves deciding satisfiability of formulas of a decidable theory, which can often be reduced to solving ...

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• (2018-07-12)
In the first part of this thesis, we follow Varopoulos's perspective to establish the noncommutaive Sobolev inequaties (namely, Hardy-Littlewood-Sobolev inequalites), and extend the Sobolev embedding from noncommutative ...

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• (2018-07-13)
In this dissertation, we discuss properties of the family of sequences $\mathbf{u_d} = \{u_d(n)\}_{n \geq 0}$ for positive integer $d$. We define them by letting $u_d(n)$ be the coefficient of $X^n$ in \$\displaystyle ...

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• (2018-07-11)
This thesis is divided into three major topics. In the first, we study questions concerning the distribution of lattice points in dimensions two and higher. We give asymptotic formulas for the number of integer lattice ...

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