Amplification arguments for large sieve inequalities
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We give a new proof of the arithmetic large sieve inequality based on an amplification argument, and use a similar method to prove a new sieve inequality for classical holomorphic cusp forms. A sample application of the latter is also given.
Mathematics Subject Classification (2000)Primary 11N35 11F11
KeywordsLarge sieve inequality Modular form Amplification
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- 4.W. Duke and E. Kowalski, A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations, with an Appendix by D. Ramakrishnan, Invent math. 139 (2000), 1–39.Google Scholar
- 5.H. Halberstam and H. E. Richert, Sieve methods, London Math. Soc. Monograph, Academic Press (London), 1974Google Scholar
- 7.H. Iwaniec and E. Kowalski, Analytic number theory, AMS Colloquium Publ. 53, 2004.Google Scholar
- 8.E. Kowalski, The large sieve and its applications: arithmetic geometry, random walks and discrete groups, Cambridge Tracts in Math. 175, 2008.Google Scholar
- 9.Y. K. Lau and J. Wu, A large sieve inequality of Elliott–Montgomery–Vaughan type for automorphic forms and two applications, International Mathematics Research Notices, Vol. 2008 , doi: 10.1093/imrn/rmn162.
- 10.H.-L. Montgomery, Topics in multiplicative number theory, Lecture Notes Math. 227, Springer-Verlag 1971.Google Scholar
- 13.P. Sarnak, Statistical properties of eigenvalues of the Hecke operators, in: Analytic Number Theory and Diophantine Problems (Stillwater, OK, 1984), Progr. Math. 70, Birkhäuser, 1987, 321–331.Google Scholar
- 15.F. Shahidi, Symmetric power L-functions for GL(2), in: Elliptic curves and related topics, E. Kishilevsky and M. Ram Murty (eds.), CRM Proc. and Lecture Notes 4, 1994, 159–182.Google Scholar