On the negative Pell equation

DOI10.4007/annals.2010.172.2035zbMath1230.11136OpenAlexW2047105323MaRDI QIDQ5894113

Étienne Fouvry, Jürgen Klüners

Publication date: 11 February 2011

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4007/annals.2010.172.2035

zbMATH Keywords

class groupsPell equationCohen-Lenstra heuristic

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29) General binary quadratic forms (11E16)

Related Items (25)

A Note on the Negative Pell Equation ⋮ Asymptotics of Class Numbers for Real Quadratic Fields ⋮ On the 16-rank of class groups of \({\mathbb{Q}(\sqrt{-8p})}\) for \({p \equiv -1 \bmod 4}\) ⋮ The 8-rank of the narrow class group and the negative Pell equation ⋮ Redei reciprocity, governing fields and negative Pell ⋮ On the 8-rank of narrow class groups of ℚ(−4pq), ℚ(−8pq), and ℚ(8pq) ⋮ On counting polynomials over finite fields ⋮ ON THE -RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS ⋮ The infinite dihedral group and K3 surfaces with Picard number 2 ⋮ On Dirichlet biquadratic fields ⋮ On 2‐Selmer groups of twists after quadratic extension ⋮ LARGE MOMENTS AND EXTREME VALUES OF CLASS NUMBERS OF INDEFINITE BINARY QUADRATIC FORMS ⋮ A POLYNOMIAL ANALOGUE OF LANDAU'S THEOREM AND RELATED PROBLEMS ⋮ Pairs of integers which are mutually squares ⋮ Explicit methods in number theory. Abstracts from the workshop held July 18--24, 2021 (hybrid meeting) ⋮ On the negative Pell equation ⋮ Hilbert genus fields of real biquadratic fields ⋮ On the period of the continued fraction of $\sqrt{pq}$ ⋮ Counting dihedral and quaternionic extensions ⋮ On the evolution of continued fractions in a fixed quadratic field ⋮ Spins of prime ideals and the negative Pell equation ⋮ Kuroda's formula and arithmetic statistics ⋮ Quaternionic Artin representations and nontraditional arithmetic statistics ⋮ SPIEGELUNGSSATZ: A COMBINATORIAL PROOF FOR THE 4-RANK ⋮ On unit signatures and narrow class groups of odd degree abelian number fields

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