Dr Kyle Pratt

Status

Affiliate Researcher

Research groups

Number Theory

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Recent publications

Dirichlet L-functions of quadratic characters of prime conductor at the central point

Baluyot, S Pratt, K Journal of the European Mathematical Society (20 Jul 2021)

Exceptional characters and nonvanishing of Dirichlet L-functions

Bui, H Pratt, K Zaharescu, A Mathematische Annalen volume 380 593-642 (06 Feb 2021)

Breaking the 1/2-barrier for the twisted second moment of Dirichlet L-functions

Bui, H Pratt, K Robles, N Zaharescu, A Advances in Mathematics volume 370 107175-107175 (01 Aug 2020)

Primes from sums of two squares and missing digits

Pratt, K Proceedings of the London Mathematical Society volume 120 issue 6 770-830 (01 Jun 2020)

Average nonvanishing of Dirichlet L-functions at
the central point

Pratt, K Algebra & Number Theory volume 13 issue 1 227-249 (13 Feb 2019)

Research interests

I work in the field of analytic number theory. My recent research has focused on prime numbers, L-functions, and Diophantine problems. You can find my papers here on the arXiv.

Further details

I have been a post-doctoral research fellow at All Souls College since October 2019. I earned my PhD in mathematics from the University of Illinois at Urbana-Champaign in May 2019.

Teaching

From April-June 2022 I taught a TCC course "The Riemann zeta function: classical roots and modern approaches." Course materials are here.

The course covered some of the classical roots of the theory of the zeta function, but with an eye towards modern research (the sorts of things less likely to appear in textbooks).

Here are some of the things we looked at: basic theory, the prime number theorem, zero-density estimates and primes in short intervals, extreme values, Selberg's central limit theorem, the work of Soundararajan on conditionally bounding high moments, computational aspects of the zeta function.