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Media type:
E-Article
Title:
Sparse equidistribution problems, period bounds and subconvexity
Contributor:
Venkatesh, Akshay
imprint:
Dept. of Mathematics, Princeton University, 2010
Published in:Annals of Mathematics
Language:
English
ISSN:
0003-486X
Origination:
Footnote:
Description:
<p>We introduce a "geometric" method to bound periods of automorphic forms. The key features of this method are the use of equidistribution results in place of mean value theorems, and the systematic use of mixing and the spectral gap. Applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of CM points; to subconvexity of the triple product period in the level aspect over number fields, which implies subconvexity for certain standard and Rankin-Selberg L-functions; and to bounding Fourier coefficients of automorphic forms.</p>