A new parametrization for ideal classes in rings defined by binary forms, and applications

DOI10.1515/crelle-2023-0006zbMath1525.11133OpenAlexW4361006948MaRDI QIDQ6042647

Ashvin A. Swaminathan

Publication date: 3 May 2023

Published in: Journal für die Reine und Angewandte Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle-2023-0006

zbMATH Keywords

binary formsideal classesinverse different\(2\)-class group\(p\)-adic density

Mathematics Subject Classification ID

Forms of degree higher than two (11E76) Class numbers, class groups, discriminants (11R29) Density theorems (11R45) Algebraic numbers; rings of algebraic integers (11R04) Class groups (13C20) Class groups and Picard groups of orders (11R65)

Related Items

Most odd-degree binary forms fail to primitively represent a square

Cites Work

• Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
• On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields
• The density of discriminants of quintic rings and fields
• On the 4-rank of class groups of quadratic number fields
• A ``class group obstruction for the equation \(Cy^d=F(x,z)\)
• Binary forms and orders of algebraic number fields
• Odd degree number fields with odd class number
• Higher composition laws. II: On cubic analogues of Gauss composition
• Squarefree values of polynomial discriminants. I
• Parametrization of ideal classes in rings associated to binary forms
• The density of discriminants of quartic rings and fields
• A canonical quadratic form for the ring of 2-adic integers
• On the Distribution of Class Groups of Number Fields
• A positive proportion of locally soluble hyperelliptic curves over ℚ have no point over any odd degree extension
• Class Groups of Number Fields: Numerical Heuristics
• Rings and ideals parameterized by binary n -ic forms
• Random maximal isotropic subspaces and Selmer groups
• Decomposition of primes in non-maximal orders
• Low-dimensional lattices. IV. The mass formula
• Rational points on hyperelliptic curves having a marked non-Weierstrass point
• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r
• $2$-Selmer groups of hyperelliptic curves with marked points
• Equality of Polynomial and Field Discriminants
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
• On the density of discriminants of cubic fields. II
• Finiteness Theorems for Binary Forms with Given Discriminant
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