Upper bounds on relative class numbers of cyclotomic fields

Year, pages: 2014, 21 - 26

We explain how one can use the explicit formulas for the mean square values of $L$-functions which we established elsewhere to obtain explcit upper bounds on relative class numbers of cyclotomic number fields. As an example, we show that the relative class numbers of the cyclotomic fields of conductor $4p$, $p≥ 3$ a prime, are less than or equal to $8\sqrt p (p/16)^(p-1)/2$.

Louboutin, S. 2014. Upper bounds on relative class numbers of cyclotomic fields. In Mathematica Slovaca, vol. 64, no.1, pp. 21-26. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0183-5

Louboutin, S. (2014). Upper bounds on relative class numbers of cyclotomic fields. Mathematica Slovaca, 64(1), 21-26. 0139-9918. DOI: https://doi.org/10.2478/s12175-013-0183-5