Voronoi formulas on GL(n)
By Dorian Goldfeld, Xiaoqing Li. 2006
80 citations recorded by the source corpus.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a2aa72991564a3263e4c3512382e2589de73961f
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- On the Voronoĭ formula for GL(n) (2013, methodology): “Voronŏı type formulas for GL(n) and full level have also been established by Goldfeld-Li [11] using the functional equations of the twisted L-functions, as in the above Duke-Iwaniec approach.”
- A general Voronoi summation formula for GL(n,Z) (2009, unknown): “ dn−2| qc1...cn−2 ...dn−3 X r6=0 ar,d n−2,...,d1 |rd1···dn−2| × ×S(r,¯a;q,c,d) F r d2 n−2 d 3 n−3···d n−1 1 qn cn−2 c2 n−3···c n−2 1 . A Voronoi summation formula for GL(n) appears in Goldfeld-Li [8,9]. Our formula precedes the Goldfeld-Li formula; see [10]. It is also more general in two respects”
- The Central value of the Rankin–Selberg L-Functions (2008, methodology): “In this paper, we consider the simultaneous nonvanishing problem of products of Rankin-Selberg on GL(3) and GL (2) and Maass Lfunctions on GL(2) at the central point 1/2.”
- On the Rankin–Selberg problem (2020, unknown): “ng ψ(y) to ψ(y/N) for a positive real number N has the effect of changing Ψ±(z) to Ψ±(zN). The Voronoi formula on GL(3) was first proved by Miller–Schmid [21]. The present version is due to Goldfeld–Li [8] with slightly renormalized variables (see Blomer [2, Lemma 3]). Lemma 13. Let c,d,d¯∈ Zwith c6= ”