Fourier coefficients of modular forms on G2

By W. Gan, B. Gross, Gordan Savin. 2002

132 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4bf3c1b222eccbc5a067c401f2e1919f396924c4

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In Algebra and Number Theory

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Citations in the corpus

Parametrization of ideal classes in rings associated to binary forms (2010, background): “For n = 3, binary cubic forms parametrize cubic rings exactly ([8], [10]).”
Higher composition laws IV: The parametrization of quintic rings (2008, background): “We are thus able to recover, from a geometric viewpoint, the celebrated result of Delone-Faddeev [11] and Gan-Gross-Savin [12] parametrizing cubic rings (as reformulated in [4]).”
Lectures on black holes, topological strings and quantum attractors (2006, background): “One can show that the result is invariant under the linear action of Conf(J, Z) on the charges, and has support only on charges with I4(pI, qI) ≥ 0 (see e.g. [ 172 ] in the case of”
Distribution of periodic torus orbits and Duke's theorem for cubic fields (2007, result): “In particular, if n is prime, µ is Haar measure on Xn. 5 Another possibility, more in line with Duke’s original proof would be to use results of Gan, Gross and Savin [23] which relate the Weyl’s sums to Fourier coefficient to automorphic forms on G2; unfortunately our state of knowledge concerning b”
Higher composition laws II: On cubic analogues of Gauss composition (2004, background): “Theorem 1 ([4],[5]).”
Secondary terms in counting functions for cubic fields (2011, methodology): “The Delone-Faddeev correspondence, which extends that of Davenport-Heilbronn and which was further extended by Gan, Gross, and Savin [17] to include the degenerate case, is as follows:”
On the Davenport–Heilbronn theorems and second order terms (2010, methodology): “We begin with a theorem of Delone–Faddeev [17] (as refined by Gan–Gross–Savin [21]) parametrizing cubic rings by GL2(Z)-equivalence classes of integral binary cubic forms.”
Higher composition laws III: The parametrization of quartic rings (2004, background): “and the latter is clearly not Gorenstein if k> 2. Gan-Gross-Savin [ 10 ] have shown that in the rank 3 case, the notions of Gorenstein and content 1 actually coincide.”
The geometric sieve and the density of squarefree values of invariant polynomials (2014, methodology): “Building on the works of Levi [32], Wright–Yukie [42], and Gan–Gross–Savin [24], it was shown in [21], [2], and [3] that the integers that occur as the discriminants of orders in cubic, quartic, and quintic number fields, respectively, correspond to suitable integer values taken by certain fixed mul”