The subconvexity problem for Artin L–functions

By William Duke, John B. Friedlander, Henryk Iwaniec. 2002

204 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d833fe03ef25a4b8baf512f0b9b7d634224eab74

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Citations in the corpus

Bounds for GL(3)×GL(2) L -functions and GL(3) L -functions (2008, methodology): “For degree two L-functions this was achieved in a series of papers by Good [Go], Meurman [Me] and especially Duke, Friedlander and Iwaniec [DFI1, DFI2, DFI3 ].”
Bounding the sup-norm of automorphic forms (2004, methodology): “Remark 3.4. The technique of embedding a basis of holomorphic forms into a basis of Maass forms has been used in other investigations; in specific arithmetic contexts regarding holomorphic forms of weight one, where no harmonic analysis is possible, this technique was used in [ DuFI ] and [MV].”
The subconvexity problem for Rankin–Selberg L-functions and equidistribution of Heegner points. II (2006, methodology): “y2 . Using the bounds of Theorem 1, [ DFI02 ] and the approximation arguments of [LS95, Sect.”
Distribution of periodic torus orbits and Duke's theorem for cubic fields (2007, background): “With F =Q, the proofs exist in print and are contained in [3], [14], and [15].”
The spectral decomposition of shifted convolution sums (2007, methodology): “This follows from Shalika’s multiplicity one theorem combined with standard facts about Hecke operators, see [CoPS, Sections 4.1 and 6.2] and [ DFI3 , (6.14)–(6.15)].”
Explicit calculations with Eisenstein series (2017, methodology): “sequences 4.1. The Fourier expansion. For k= 0, Huxley [Hux] stated (without proof) the Fourier expansion of Eχ1,χ2(z,s); a proof may be found in [KL, Section 5.6]. For general k, and χ1χ2 primitive, [DFI] have developed the Fourier expansion. One may also ﬁnd a Fourier expansion for Eχ1,χ2,k in [DS”
A general Voronoi summation formula for GL(n,Z) (2009, background): “hday 1. Introduction The Voronoi summation formulas for GL(2) and GL(3) have had numerous applications to problems in analytic number theory, perhaps most notably to recent subconvexity results (e.g. [1,6,15,16,20]). The formulas provide an identity between sums of the form X m∈Z am e 2πimα f(m) = X”
The subconvexity problem for GL2 (2009, background): “— The bound generalizes (up to the value of δ) a variety of subconvex bounds [71,12,29,27,47,17,18,64,22,34,19,42,44,48,6,54,31,9,8, 67,16].”
Hybrid bounds for twisted L-functions (2008, background): “for some o ¼ oðgÞ of modulus 1, cf. [ DFI ], (8.11)–(8.13), (8.17)–(8.19).”