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Imaginary quadratic fields with p-torsion-free class groups and specified split primes

Number Theory Seminar
April 8, 2024
4:00 pm - 5:00 pm
MW 154

Title:  Imaginary quadratic fields with p-torsion-free class groups and specified split primes

Speaker:  Olivia Beckwith (Tulane University)

Abstract:  We study Ramanujan-type congruences for Hurwitz class numbers using harmonic Maass forms. As an application, we show that for any odd prime p and finite set of odd primes S, there exists an imaginary quadratic field which splits at each prime in S and has class number indivisible by p. This result is in the spirit of results by Bruinier, Bhargava (when p=3) and Wiles, but the methods are completely different. This is joint work with Martin Raum and Olav Richter.

URL associated with Seminar:  https://research.math.osu.edu/numbertheory/

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Seminar - Number Theory