Strong orthogonality between the Möbius function, additive characters and Fourier coefficients of cusp forms

Étienne Fouvry, Satadal Ganguly

Type: Article

Publication Date: 2014-04-24

Citations: 27

DOI: https://doi.org/10.1112/s0010437x13007732

Abstract

Abstract Let $\nu _{f}(n)$ be the $n\mathrm{th}$ normalized Fourier coefficient of a Hecke–Maass cusp form $f$ for ${\rm SL }(2,\mathbb{Z})$ and let $\alpha $ be a real number. We prove strong oscillations of the argument of $\nu _{f}(n)\mu (n) \exp (2\pi i n \alpha )$ as $n$ takes consecutive integral values.

Locations

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+	Introduction to the spectral theory of automorphic forms	1995	Henryk Iwaniec
+	None	2003	Farrell Brumley
+	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
+ PDF Chat	On the prime number theorem for the coefficients of certain modular forms	1985	Alberto Perelli
+	Topics in Classical Automorphic Forms	1997	Henryk Iwaniec
+	Automorphic forms and representations	1997	Daniel Bump
+	Disjointness of Moebius from Horocycle Flows	2012	Jean Bourgain Peter Sarnak Tamar Ziegler
+	None	1995	Jeffrey Hoffstein Dinakar Ramakrishnan
+	Summation formulas, from Poisson and Voronoi to the present	2004	Stephen D. Miller Wilfried Schmid