Imaginary Quadratic Fields With ℓ-Torsion-Free Class Groups and Specified Split Primes
Journal article, 2024

Given an odd prime $\ell $ and finite set of odd primes $S_{+}$ , we prove the existence of an imaginary quadratic field whose class number is indivisible by $\ell $ and which splits at every prime in $S_{+}$ . Notably, we do not require that $p \not \equiv -1 \,\;(\mathrm{mod}\, \ell )$ for any of the split primes $p$ that we impose. Our theorem is in the spirit of a result by Wiles, but we introduce a new method. It relies on a significant improvement of our earlier work on the classification of non-holomorphic Ramanujan-type congruences for Hurwitz class numbers.

Author

Olivia Beckwith

Tulane University

Martin Raum

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

Olav K. Richter

University of North Texas

Published in

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)

Vol. 2024 Issue 16 p. 11582-11596

Research Project(s)

Real-Analytic Orthogonal Modular Forms as Generating Series

Swedish Research Council (VR) (2019-03551), 2020-01-01 -- 2023-12-31.

Categorizing

Subject Categories (SSIF 2011)

Mathematical Analysis

Identifiers

DOI

10.1093/imrn/rnae130

More information

Latest update

9/7/2024 4