Caliber numbers of real quadratic fields

2011/11/29 by Byungheup Jun, Jungyun Lee, Jun, Byungheup +1
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Limits and Structures in Graph Theory #math.NT

paper · pdf · doi:10.48550/arxiv.1111.6718

10 pages

arxiv created 2011/11/29 · arxiv updated 2011/11/30

Abstract

We obtain lower bound of caliber number of real quadratic field K=\FQ(√(d)) using splitting primes in K. We find all real quadratic fields of caliber number 1 and find all real quadratic fields of caliber number 2 if d is not 5 modulo 8. In both cases, we don't rely on the assumption on ζ_K(1/2).

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