On Gerth’s heuristics for a family of quadratic extensions of certain Galois number fields

Authors

• C. G.K. Babu, Indian Statistical Institute, Kolkata
• R. Bera, Indian Statistical Institute (Delhi Centre)
• J. Sivaraman, Indian Institute of Science Education and Research Thiruvananthapuram
• B. Sury, Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Ramanujan Journal

Abstract

Gerth generalised Cohen–Lenstra heuristics to the prime p=2. He conjectured that for any positive integer m, the limit (Formula presented.) exists and proposed a value for the limit. Gerth’s conjecture was proved by Fouvry and Kluners in 2007. In this paper, we generalize their result by obtaining lower bounds for the average value of |ClL2/ClL4|m, where L varies over an infinite family of quadratic extensions of certain Galois number fields. As a special case of our theorem we obtain lower bounds for the average value of |ClL2/ClL4|m as we vary L in an infinite family of quadratic extensions of certain Galois number fields of class number 1 containing Q(i).

DOI

10.1007/s11139-025-01146-y

Publication Date

9-1-2025

Recommended Citation

Babu, C. G.K.; Bera, R.; Sivaraman, J.; and Sury, B., "On Gerth’s heuristics for a family of quadratic extensions of certain Galois number fields" (2025). Journal Articles. 5490.
https://digitalcommons.isical.ac.in/journal-articles/5490