Limit theorems for theta sums

Duke Mathematical Journal

Volumn 97, Issue 1, 1999, Pages 127-153

  Marklof, Jens ^a,b,c  

^a PRINCETON UNIVERSITY   (United States)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

^c 91405 Orsay Campus   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033558658     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-09706-5     Document Type: Article

References (19)

1. M. V. Berry and J. Goldberg, Renormalisation of curlicues, Nonlinearity 1 (1988), 1-26.
2. F. M. Dekking and M. Mendès France, Uniform distribution modulo one: A geometrical viewpoint, J. Reine Angew. Math. 329 (1981), 143-153.
3. G. H. Hardy and J. E. Littlewood, Some problems in diophantine approximation, II, Acta Math. 37 (1914), 193-239.
4. G. H. Hardy and J. E. Littlewood, A further note on the trigonometrical series associated with the elliptic $-functions, Proc. Cambridge Philos. Soc. 21 (1923), 1-5.
5. D. Hejhal, The Selberg Trace Formula for PSL(2, R), Vol. 2, Lect. Notes in Math. 1001, Springer-Verlag, Berlin, 1983.
6. D. Hejhal, “On value distribution properties of automorphic functions along closed horocycles” in XVIthRolfNevanlinna Colloquium (Joensuu, 1995), de Gruyter, Berlin, 1996, 39-52.
7. E. Hopf, Statistik der geodatischen Linien in Mannigfaltigkeiten negativer Krümmung, Ber. Verh. Sachs. Akad. Wiss. Leipzig 91 (1939), 261-304.
8. W. B. Jurkat and J. W. van Horne, The proof of the central limit theorem for theta sums, Duke Math. J. 48 (1981), 873-885.
9. W. B. Jurkat and J. W. van Horne, On the central limit theorem for theta series, Michigan Math. J. 29 (1982), 65-77.
10. W. B. Jurkat and J. W. van Horne, The uniform central limit theorem for theta sums, Duke Math. J. 50 (1983), 649-666.
11. G. Lion and M. Vergne, The Weil Representation, Maslov Index and Theta Series, Progr. In Math. 6, Birkhauser, Boston, 1980.
12. J. Marklof, “Theta sums, Eisenstein series, and the semiclassical dynamics of a precessing spin” in Emerging Applications of Number Theory, ed. D. Hejhal et al., IMA Vol. Math. Appl. 109, Springer-Verlag, New York, 1998, 405-450.
13. P. Sarnak, Asymptotic behavior of periodic orbits of the horocycle flow and Eisenstein series, Comm. Pure Appl. Math. 34 (1981), 719-739.
14. P. Sarnak, Class numbers of indefinite binary quadratic forms, J. Number Theory 15 (1982), 229-247.
15. G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Kanô Memorial Lectures 1, Publ. Math. Soc. Japan 11, Iwanami Shoten, Tokyo; Princeton Univ. Press, Princeton, 1971.
16. G. Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440-481.
17. G. Shimura, On the transformation formulas of theta series, Amer. J. Math. 115 (1993), 1011-1052.
18. T. Shintani, On construction of holomorphic cusp forms of half integral weight, Nagoya Math. J. 58 (1975), 83-126.
19. S. Thangavelu, Lectures on Hermite and Laguerre Expansions, Math. Notes 42, Princeton Univ. Press, Princeton, 1993.