Higher composition laws

By Manjul Bhargava. 2001

81 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e5e82b4749102a4a5e1e38042e36862207048fd9

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Citations in the corpus

Local-global principles for representations of quadratic forms (2006, background): “This is very likely related to the composition laws presented in [3], [4], and seems likely to suggest further composition laws on integral orbit spaces.”
Parametrization of ideal classes in rings associated to binary forms (2010, methodology): “As in [1, 2], we must define a notion of balanced to state a more general theorem.”
Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves (2010, methodology): “It is proven in [2] that the orbit space (GL2(Z)×SL3(Z))\WZ corresponds to isomorphism classes of pairs (Q,R), where Q is a quartic ring”
Counting extensions of function fields with bounded discriminant and specified Galois group (2005, methodology): “Counting extensions of function fields with bounded discriminant and specified Galois group Jordan S. Ellenberg and Akshay Venkatesh∗ 29 Apr 2004”
The 3‐part of Class Numbers of Quadratic Fields (2005, background): “) More generally, Yamamoto [70] and Weinberger [68] have shown that there are infinitely many real quadratic fields with class number divisible 2In [10], Cohen and Martinet provide analogous heuristics for number fields of higher degree, recently verified in the case of the mean size of the 2-class ”
The number of extensions of a number field with fixed degree and bounded discriminant (2003, background): “A folk conjecture, possibly due to Linnik, asserts that NK,n(X) ∼ cK,nX (n fixed, X → ∞) This conjecture is trivial when n = 2; it has been proved for n = 3 by Davenport and Heilbronn [6] in case K = Q, and by Datskovsky and Wright in general [5]; and for n = 4, 5 and K = Q by Bhargava [2],[1].”