Browsing Mathematics (Faculty of) by Subject "Number Theory"
Now showing items 16 of 6

Exact Formulas for Averages of Secular Coefficients
(University of Waterloo, 20210929)We study averages of secular coefficients that frequently appear in random matrix theory. We obtain exact formulas, identities and new asymptotics for these integrals as well as a technique to deal with singularities that ... 
HigherDimensional Kloosterman Sums and the Greatest Prime Factor of Integers of the Form a_1a_2\cdots a_{k+1}+1
(University of Waterloo, 20070829)We consider the greatest prime factors of integers of certain form. 
Koblitz's Conjecture for the Drinfeld Module
(University of Waterloo, 20080501)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 Lfunctions
(University of Waterloo, 20110617)<p>Given a positive integer k, Conrey, Farmer, Keating, Rubinstein and Snaith conjectured a formula for the asymptotics of the kth moments of the central values of quadratic Dirichlet Lfunctions. The conjectured formula ... 
The Normal Distribution of ω(φ(m)) in Function Fields
(University of Waterloo, 20080128)Let ω(m) be the number of distinct prime factors of m. A celebrated theorem of ErdösKac states that the quantity (ω(m)loglog m)/√(loglog m) distributes normally. Let φ(m) be Euler's φfunction. Erdös and Pomerance ... 
Using Automata Theory to Solve Problems in Additive Number Theory
(University of Waterloo, 20180430)Additive number theory is the study of the additive properties of integers. Perhaps the bestknown theorem is Lagrange’s result that every natural number is the sum of four squares. We study numbers whose basek representations ...