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#### Higher-Dimensional Kloosterman Sums and the Greatest Prime Factor of Integers of the Form a_1a_2\cdots a_{k+1}+1

(University of Waterloo, 2007-08-29)

We consider the greatest prime factors of integers of certain form.

#### The Normal Distribution of ω(φ(m)) in Function Fields

(University of Waterloo, 2008-01-28)

Let ω(m) be the number of distinct prime factors of m. A
celebrated theorem of Erdös-Kac states that the quantity
(ω(m)-loglog m)/√(loglog m) distributes
normally. Let φ(m) be Euler's φ-function. Erdös and
Pomerance ...

#### Koblitz's Conjecture for the Drinfeld Module

(University of Waterloo, 2008-05-01)

Let $E$ be an elliptic curve over the rationals without complex multiplication such that any elliptic curve $\mathbb{Q}$-isogenous to $E$ has trivial $\mathbb{Q}$-torsion. Koblitz conjectured that the number of primes less ...

#### Lower order terms of moments of L-functions

(University of Waterloo, 2011-06-17)

<p>Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the k-th moments of the central values of quadratic Dirichlet L-functions. The conjectured formula ...