Caliber numbers of real quadratic fields

Details Caliber numbers of real quadratic fields Caliber numbers of real quadratic fields

2011-11-29

arxiv.org/abs/1111.6718v1

Mathematics

Number Theory

10 pages

Scientific paper

We obtain lower bound of caliber number of real quadratic field
$K=\FQ(\sqrt{d})$ 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
$\zeta_K(1/2)$.

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