Department of Mathematics
Fine
Hall
Princeton University
Princeton, NJ 08544
lbpierce_at_princeton_dot_edu
Research Interests
Harmonic Analysis
I am currently working on discrete analogues in harmonic analysis. I have proved results for broad classes of families, ranging from twisted discrete singular Radon transforms to discrete fractional integral operators along quadratic surfaces and a discrete analogue of fractional integration on the Heisenberg group. The techniques I am developing require intricate number theoretic methods as well as substantial analytic machinery.
Number Theory
In analytic number theory, I have made progress on a long-standing problem relating to class numbers of quadratic fields, proving several nontrivial bounds for the 3-part of such class numbers via variants of Burgess' method, the square sieve, and the q-analogue of van der Corput's method. My interests include the circle method, sieves, exponential sums, quadratic forms, and Burgess' method.
Future Research
I ultimately plan to work as a number theorist, using analytic techniques. Future research plans include projects on exponential and character sums, and on restriction theorems for automorphic forms.
