A variant of Brun-Titchmarsh for the Chebotarev density theorem
Asif Zaman, University of Toronto
Asif Zaman, University of Toronto
Sacha Mangerel, University of Toronto
Kevin Hare, Department of Pure Mathematics, University of Waterloo
Alexander Dahl, York University
Patrick Ingram, York University
Youness Lamzouri, York University
The study of class numbers of real and imaginary quadratic fields
in an important problem in number theory, and its rich history
goes back to the work of Gauss. In this talk, I will review the
history of this subject and present recent results on these class
numbers, notably on their large values, moments and distribution.
M3 3103
Roger Baker, Brigham Young University
Let ||...|| denote distance from the nearest integer. Let f be a quadratic polynomial with irrational leading coefficient. We give a new result on small values of ||f(p)|| for infinitely many primes p. One technique that is used involves a lemma of Birch and Davenport on a real number with many rational approximations, and I will try to explain the role of this lemma in the work.
M3 3103
Oleksiy Klurman, University College London
David Tweedle, The University of the West Indies
Recall Artin's primitive root conjecture, which states that if a is not -1 or a square then the reduction of a modulo p generates the multiplicative group of the integers modulo p for infinitely many primes p. We will examine the similarities and differences between Artin's conjecture and some natural analogues for elliptic curves and function fields.
MC 5403
Julia Brandes, Department of Pure Mathematics, University of Waterloo
"Optimal mean value estimates beyond Vinogradov's mean value theorem"