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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm162, 35 pages, doi:10.1093/imrn/rnm162 published on February 11, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

A Large Sieve Inequality of Elliott–Montgomery–Vaughan Type for Automorphic Forms and Two Applications

Y.-K. Lau1 and J. Wu2,3,

1 Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
2 Institut Elie Cartan Nancy (IECN), Nancy-Université, CNRS, INRIA, Boulevard des Aiguillettes, B.P. 239, 54506, Vandœuvre-lès-Nancy, France
3 School of Mathematical Sciences, Shandong, Normal University, Jinan, Shandong 250014, China

Correspondence: Correspondence to be sent to: yklau{at}maths.hku.hk

In this paper, we establish a large sieve inequality of Elliott–Montgomery–Vaughan type for Fourier coefficients of newforms. As applications, we give a significant improvement on the principal result of Duke and Kowalski on Linnik's problem for modular forms and prove the upper part of the first conjecture of Montgomery–Vaughan in the context of automorphic L-functions.


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