Cohen–Lenstra Heuristics of Quadratic Number Fields

Fouvry, Étienne; Klüners, Jürgen

doi:10.1007/11792086_4

Cited by 44 publications

(77 citation statements)

References 6 publications

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“…From the asymptotic expansions of these moments for any integral order k, we deduce Theorems 1 & 2 as it was done in [6], [8] & [9], using tools presented in [7]. This completes the proof of these theorems.…”

Section: éTienne Fouvry and Jürgen Klünerssupporting

confidence: 53%

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Weighted Distribution of the 4-rank of Class Groups and Applications

Fouvry¹,

Klüners²

2010

International Mathematics Research Notices

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Abstract. We prove that the distribution of the values of the 4-rank of ideal class groups of quadratic fields is not affected when it is weighted by a divisor type function. We then give several applications concerning a new lower bound of the sums of class numbers of real quadratic fields with discriminant less than a bound tending to infinity and several questions of P. Sarnak concerning reciprocal geodesics.

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Section: éTienne Fouvry and Jürgen Klünerssupporting

confidence: 53%

“…Similar statements remain true if one restricts the summation over D to one of the congruence classes written in (7) in the case of (11) and (12), and to one of the congruence classes written in (8) in the case of (13) and (14).…”

mentioning

confidence: 57%

Weighted Distribution of the 4-rank of Class Groups and Applications

Fouvry¹,

Klüners²

2010

International Mathematics Research Notices

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“…We can use the same approach for our six subfamilies as in the proofs of [Fouvry and Klüners 2006, Theorems 1 and 2]. Altogether, we get the following result, which extends [Fouvry and Klüners 2007, Theorem 3] to the six families.…”

Section: General Results On the 4-ranksupporting

confidence: 54%

On the Spiegelungssatz for the 4-rank

Fouvry

Klüners

2010

ANT

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“…This paragraph uses analytic and combinatorial methods. The strategy is similar to [10,4] (see also [18,8]). Our first step is to work with Theorem 3 only, to deduce, roughly speaking, the value of ı.a; a/Cı.a; a 1/, without proving the existence of the terms of this sum (for more precisions, see (21) below).…”

Section: 4mentioning

confidence: 99%