Now showing items 1-6 of 6

    • Exact Formulas for Averages of Secular Coefficients 

      Medjedovic, Andean (University of Waterloo, 2021-09-29)
      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 ...
    • Higher-Dimensional Kloosterman Sums and the Greatest Prime Factor of Integers of the Form a_1a_2\cdots a_{k+1}+1 

      Wu, Shengli (University of Waterloo, 2007-08-29)
      We consider the greatest prime factors of integers of certain form.
    • Koblitz's Conjecture for the Drinfeld Module 

      Jain, Lalit Kumar (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 

      Rishikesh (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 ...
    • The Normal Distribution of ω(φ(m)) in Function Fields 

      Li, Li (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 ...
    • Using Automata Theory to Solve Problems in Additive Number Theory 

      Rajasekaran, Aayush (University of Waterloo, 2018-04-30)
      Additive number theory is the study of the additive properties of integers. Perhaps the best-known theorem is Lagrange’s result that every natural number is the sum of four squares. We study numbers whose base-k representations ...


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