2019
DOI: 10.48550/arxiv.1911.13115
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Successive maxima of the non-genus part of class numbers

Georges Gras

Abstract: Some PARI programs have bringed out a property for the non-genus part of the class number of the imaginary quadratic fields, with respect to ( √ D ) ε , where D is the absolute value of the discriminant and ε ∈]0, 1[, in relation with the ε-conjecture. The general Conjecture 3.1, restricted to quadratic fields, states that, for ε ∈]0, 1[, the successive maxima, as D increases, of, where H is the class number and N the number of ramified primes, occur only for prime discriminants (i.e., H odd); we perform compu… Show more

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