Imaginary Quadratic Fields With ℓ-Torsion-Free Class Groups and Specified Split Primes
Artikel i vetenskaplig tidskrift, 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.


Olivia Beckwith

Tulane Univ, Math Dept

Martin Raum

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Olav K. Richter

University of North Texas

International Mathematics Research Notices

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

Vol. In Press

Real-analytiska ortogonala modulära former som genererande serier

Vetenskapsrådet (VR) (2019-03551), 2020-01-01 -- 2023-12-31.


Matematisk analys



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