Sieving for mass equidistribution

We approach the holomorphic analogue to the Quantum Unique Ergodicity conjecture through an application of the Large Sieve. We deal with shifted convolution sums as in [Hol09], with various simplifications in our analysis due to the knowledge of the Ramanujan-Petersson conjecture in this holomorphic...

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Veröffentlicht in:	Annals of mathematics 2010-09, Vol.172 (2), p.1499-1516
1. Verfasser:	Holowinsky, Roman
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Eigenvalues Exact sciences and technology Fourier coefficients Fourier series Fourier series expansion General mathematics General, history and biography Global analysis, analysis on manifolds Inner products Integers Limit theorems Mathematical functions Mathematics Number theory Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Series convergence Series expansion Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Zusammenfassung:	We approach the holomorphic analogue to the Quantum Unique Ergodicity conjecture through an application of the Large Sieve. We deal with shifted convolution sums as in [Hol09], with various simplifications in our analysis due to the knowledge of the Ramanujan-Petersson conjecture in this holomorphic case.
ISSN:	0003-486X 1939-8980
DOI:	10.4007/annals.2010.172.1499