Fourier expansion of light‐cone Eisenstein series

Dubi Kelmer, Shucheng Yu

Type: Article

Publication Date: 2023-08-11

Citations: 2

DOI: https://doi.org/10.1112/jlms.12805

Abstract

Abstract In this work, we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic ‐space. As a consequence, we obtain results on location of all poles of these Eisenstein series as well as their supremum norms. We use this information to get new results on counting rational points on spheres.

Locations

Journal of the London Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF
Uppsala University Publications (Uppsala University) - View - PDF

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Works Cited by This (32)

Action	Title	Year	Authors
+ PDF Chat	Eisenstein series on four-dimensional hyperbolic space	1994	Valeri A. Gritsenko Rainer Schulze‐Pillot
+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec
+ PDF Chat	A new form of the circle method, and its application to quadratic forms.	1996	D. R. Heath‐Brown
+ PDF Chat	A note on the sup norm of Eisenstein series	2018	Matthew P. Young
+ PDF Chat	The arithmetic and geometry of some hyperbolic three manifolds	1983	Peter Sarnak
+	Eisenstein-series on the four-dimensional hyperbolic space	1988	Aloys Krieg
+	The mean square of the Dedekind zeta function in quadratic number fields	1989	Wolfgang Müller
+ PDF Chat	Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations	1993	Roger Howe Eng-Chye Tan
+ PDF Chat	Density of integer points on affine homogeneous varieties	1993	William Duke Zeév Rudnick Peter Sarnak
+	Eisenstein matrix and existence of cusp forms in rank one symmetric spaces	1993	Andrei Reznikov