The role of the Ramanujan conjecture in analytic number theory

Valentin Blomer, Farrell Brumley

Type: Article

Publication Date: 2013-01-14

Citations: 34

DOI: https://doi.org/10.1090/s0273-0979-2013-01404-6

Abstract

We discuss progress towards the Ramanujan conjecture for the group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper G normal upper L Subscript n"> <mml:semantics> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">G</mml:mi> <mml:mi mathvariant="normal">L</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">\mathrm {GL}_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and its relation to various other topics in analytic number theory.

Locations

Bulletin of the American Mathematical Society - View - PDF

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Works Cited by This (141)

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+	Notes on the Generalized Ramanujan Conjectures	2005	Peter Sarnak
+	The Lowest Eigenvalue for Congruence Groups	1996	Henryk Iwaniec
+	Langlands Functoriality Conjecture and Number Theory	2007	Freydoon Shahidi
+	Automorphic forms on Adele groups	1975	Stephen Gelbart
+	Automorphic Forms and L-Functions for the Group Gl(n, R)	2006	Dorian Goldfeld
+	Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂	2002	Henry Kim
+	The Geometry and Cohomology of Some Simple Shimura Varieties.	2001	Michael Harris Richard Taylor Vladimir G. Berkovich
+	On Linnik and Selberg’s Conjecture About Sums of Kloosterman Sums	2009	Peter Sarnak Jacob Tsimerman
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+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec