International audienceWe 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√p(p/16)(p−1)/2
Abstract. In the previous paper [8], the author gave a determinant for-mula of relative zeta functio...
Kummer's conjecture predicts the asymptotic growth of the relative class number of $\mathbb Q(\zet...
For any square-free positive integer m, let H(m) be the class-number of the field Q(ςm+ςm-1 ), where...
International audienceWe explain how one can use the explicit formulas for the mean square values of...
International audienceUsing formulas for quadratic mean values of L-functions at s = 1, we recover p...
International audienceUsing formulas for quadratic mean values of L-functions at s = 1, we recover p...
International audienceExplicit formulas for the quadratic mean value at s = 1 of the Dirichlet L-fun...
Let h(-)(p) be the relative class number of the p-th cyclotomic field. We show that log h(-) (p) = p...
Let h(-)(p) be the relative class number of the p-th cyclotomic field. We show that log h(-) (p) = p...
Let p be an odd prime number, and l a prime number with l ≠ p. Let h_n^− be the relative class numbe...
Class groups---and their size, the class number---give information about the arithmetic within a fie...
AbstractIn the first part of the paper we show how to construct real cyclotomic fields with large cl...
An explicit formula for the mean value of |L(1, χ)| 2 is known, where χ runs over all odd primitive ...
AbstractWe give explicit upper bounds for residues at s=1 of Dedekind zeta functions of number field...
summary:For any square-free positive integer $m\equiv {10}\pmod {16}$ with $m\geq 26$, we prove that...
Abstract. In the previous paper [8], the author gave a determinant for-mula of relative zeta functio...
Kummer's conjecture predicts the asymptotic growth of the relative class number of $\mathbb Q(\zet...
For any square-free positive integer m, let H(m) be the class-number of the field Q(ςm+ςm-1 ), where...
International audienceWe explain how one can use the explicit formulas for the mean square values of...
International audienceUsing formulas for quadratic mean values of L-functions at s = 1, we recover p...
International audienceUsing formulas for quadratic mean values of L-functions at s = 1, we recover p...
International audienceExplicit formulas for the quadratic mean value at s = 1 of the Dirichlet L-fun...
Let h(-)(p) be the relative class number of the p-th cyclotomic field. We show that log h(-) (p) = p...
Let h(-)(p) be the relative class number of the p-th cyclotomic field. We show that log h(-) (p) = p...
Let p be an odd prime number, and l a prime number with l ≠ p. Let h_n^− be the relative class numbe...
Class groups---and their size, the class number---give information about the arithmetic within a fie...
AbstractIn the first part of the paper we show how to construct real cyclotomic fields with large cl...
An explicit formula for the mean value of |L(1, χ)| 2 is known, where χ runs over all odd primitive ...
AbstractWe give explicit upper bounds for residues at s=1 of Dedekind zeta functions of number field...
summary:For any square-free positive integer $m\equiv {10}\pmod {16}$ with $m\geq 26$, we prove that...
Abstract. In the previous paper [8], the author gave a determinant for-mula of relative zeta functio...
Kummer's conjecture predicts the asymptotic growth of the relative class number of $\mathbb Q(\zet...
For any square-free positive integer m, let H(m) be the class-number of the field Q(ςm+ςm-1 ), where...
DOI
Add to ORKG