Indivisibility Of Class Numbers Research Articles

Indivisibility of class numbers of imaginary quadratic fields

We quantify a recent theorem of Wiles on class numbers of imaginary quadratic fields by proving an estimate for the number of negative fundamental discriminants down to -X whose class numbers are indivisible by a given prime ell and whose imaginary quadratic fields satisfy any given set of local conditions. This estimate matches the best results in the direction of the Cohen–Lenstra heuristics for the number of imaginary quadratic fields with class number indivisible by a given prime. This general result is applied to study rank 0 twists of certain elliptic curves.

Coefficients of half-integral weight modular forms and indivisibility of class numbers of imaginary quadratic fields

In this paper, we investigate the nonvanishing coefficients of half-integral weight modular forms modulo a prime. We also consider the indivisibility of class numbers of imaginary quadratic fields.

Indivisibility of Class Numbers and Iwasawa λ-Invariants of Real Quadratic Fields

Let D>0 be the fundamental discriminant of a real quadratic field, and h(D) its class number. In this paper, by refining Ono's idea, we show that for any prime p>3, ♯{0 >p√(X)/logX.