Weak subconvexity for central values of L-functions

Annals of Mathematics

Volumn 172, Issue 2, 2010, Pages 1469-1498

  Soundararajan, Kannan ^a  

^a STANFORD UNIVERSITY   (United States)

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EID: 77957714268     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. J. Bernstein and A. Reznikov, Periods, subconvexity of L-functions and representation theory, J. Differential Geom. 70 (2005), 129-141.
2. S. Böcherer, P. Sarnak, and R. Schulze-Pillot, Arithmetic and equidistribution of measures on the sphere, Comm. Math. Phys. 242 (2003), 67-80.
3. F. Brumley, Effective multiplicity one on GLN and narrow zero-free regions for Rankin-Selberg L-functions, Amer. J. Math. 128 (2006), 1455-1474.
4. J. Cogdell and P. Michel, On the complex moments of symmetric power L-functions at s D 1, Int. Math. Res. Not. 2004 (2004), 1561-1617.
5. P. D. T. A. Elliott, Extrapolating the mean-values of multiplicative functions, Nederl. Akad. Wetensch. Indag. Math. 51 (1989), 409-420.
6. P. B. Garrett, Decomposition of Eisenstein series: Rankin triple products, Ann. of Math. 125 (1987), 209-235.
7. d), Geom. Funct. Anal. 13 (2003), 992-1028.
8. A. Granville and K. Soundararajan, Decay of mean values of multiplicative functions, Canad. J. Math. 55 (2003), 1191-1230.
9. A. Granville and K. Soundararajan, Large character sums: pretentious characters and the Pólya-Vinogradov theorem, J. Amer. Math. Soc. 20 (2007), 357-384.
10. A. Granville and K. Soundararajan, Pretentious multiplicative functions and an inequality for the zeta-function, in Anatomy of Integers, CRM Proc. Lecture Notes 46, Amer. Math. Soc., Providence, RI, 2008, pp. 191-197.
11. G. Halász, On the distribution of additive and the mean values of multiplicative arithmetic functions, Studia Sci. Math. Hungar. 6 (1971), 211-233.
12. G. Halász, On the distribution of additive arithmetic functions, Acta Arith. 27 (1975), 143-152.
13. G. Harcos, Uniform approximate functional equation for principal L-functions, Int. Math. Res. Not. 2002 (2002), 923-932.
14. D. R. Heath-Brown, Convexity bounds for L-functions, Acta Arith. 136 (2009), 391-395.
15. A. Hildebrand, A note on Burgess' character sum estimate, C. R. Math. Rep. Acad. Sci. Canada 8 (1986), 35-37.
16. A. Hildebrand, On Wirsing's mean value theorem for multiplicative functions, Bull. London Math. Soc. 18 (1986), 147-152.
17. R. Holowinsky, Sieving for mass equidistribution, Ann. of Math. 172 (2010), 1499-1516.
18. R. Holowinsky and K. Soundararajan, Mass equidistribution of Hecke eigenforms, Ann. of Math. 172 (2010), 1517-1528.
19. H. Iwaniec, Spectral Methods of Automorphic Forms, second ed., Grad. Stud. Math. 53, Amer. Math. Soc., Providence, RI, 2002.
20. H. Iwaniec and E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Colloq. Publ. 53, Amer. Math. Soc., Providence, RI, 2004.
21. H. Iwaniec and P. Sarnak, Perspectives on the analytic theory of L-functions, Geom. Funct. Anal. Special Volume, Part II (2000), 705-741.
22. X. Li, Bounds for GL(3)×GL(2) L-functions and GL.3/ L-functions, Ann. of Math., to appear.
23. E. Lindenstrauss, Invariant measures and arithmetic quantum unique ergodicity, Ann. of Math. 163 (2006), 165-219.
24. W. Luo, Values of symmetric square L-functions at 1, J. Reine Angew. Math. 506 (1999), 215-235.
25. W. Luo, Z. Rudnick, and P. Sarnak, On Selberg's eigenvalue conjecture, Geom. Funct. Anal. 5 (1995), 387-401.
26. W. Luo and P. Sarnak, Mass equidistribution for Hecke eigenforms, Comm. Pure Appl. Math. 56 (2003), 874-891.
27. P. Michel, Analytic number theory and families of automorphic L-functions, in Automorphic Forms and Applications, IAS/Park City Math. Ser. 12, Amer. Math. Soc., Providence, RI, 2007, pp. 181-295.
28. G. Molteni, Upper and lower bounds at s D 1 for certain Dirichlet series with Euler product, Duke Math. J. 111 (2002), 133-158.
29. Z. Rudnick and P. Sarnak, The behaviour of eigenstates of arithmetic hyperbolic manifolds, Comm. Math. Phys. 161 (1994), 195-213.
30. Z. Rudnick and P. Sarnak, Zeros of principal L-functions and random matrix theory, Duke Math. J. 81 (1996), 269-322.
31. 2.Z/nH, Ann. of Math. 172 (2010), 1529-1538.
32. A. Venkatesh, Sparse equidistribution problems, period bounds, and subconvexity, Ann. of Math. 172 (2010), 989-1094.
33. T. C. Watson, Rankin triple products and quantum chaos, ProQuest LLC, Ann Arbor, MI, 2002, Ph. D. thesis, Princeton University.