Theta liftings and Hecke L-functions

Journal fur die Reine und Angewandte Mathematik

Volumn 485, Issue , 1997, Pages 25-53

  Yang, Tonghai ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

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[No Author keywords available]

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EID: 0031498488     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. S. Brocco, On the non-vanishing of θ-liftings from U(1) to U(1), Ph. D. thesis, Brandeis University, 1992.
2. S. Gelbart, I. Piatetski-Shapiro and S. Rallis, Explicit Constructions of Automorphic L-functions, Lect. Notes Math. 1254, Springer-Verlag, 1987.
3. B. Gross, Arithmetic on elliptic curves with complex multiplication, Lect. Notes Math. 776, Springer-Verlag, 1980.
4. Jiandong Guo, On the positiveness of the central critical values of automorphic L-functions for GL(2), Duke J. Math. 83 (1996), 157-190.
5. M. Harris, Non-vanishing of L-function of 2 × 2 unitary groups, Forum Math. (1993), 405-423.
6. M. Harris, L-functions of 2 × 2 unitary groups and factorization of periods of Hilbert modular forms, J. AMS 6 (1993), 627-719.
7. M. Harris, S. Kudla and W. Sweet, Theta dichotomy for unitary groups, preprint 1994.
8. S. Kudla, Splitting metaplectic covers of dual reductive pairs, Israel J. Math. 87 (1992), 361-401.
9. S. Kudla, Some extensions of the Siegel-Weil formula, J. AMS., to appear.
10. S. Kudla, On the local θ-correspondence, Invent. Math. 83 (1986), 229-255.
11. S. Kudla, Seesaw dual reductive pairs, in: Automorphic forms of several variables, Taniguchi symposium (Katata, 1983), Birkhäuser, Boston 1984.
12. S. Kudla and S. Rallis, On the Weil-Siegel Formula, J. reine angew. Math. 387 (1988), 1-68.
13. S. Kudla and S. Rallis, A regularized Siegel-Weil formula: The first term identity, Ann. Math. 140 (1994), 1-80.
14. S. Kudla and W. Sweet Jr., Degenerate principal series representation for U(n,n), preprint 1994.
15. Jian-shu Li, Non-vanishing theorems for cohomology of certain arithmetic quotients, J. reine, angew. Math. 428 (1992), 177-217.
16. C. Moen, The dual pair (U(3), U(1)) over a p-adic field, Pacific J. Math. 127 (1987), 141-154.
17. S. Rallis, Injectivity properties of liftings associated to Weil representations, Comp. Math. 52 (1984), 136-169.
18. S. Rallis, L-functions and oscillator representation, Lect. Notes Math. 1245, Springer-Verlag, 1987.
19. R. R. Rao, On some explicit formulas in the theory of Weil representations, Pacific J. Math. 157 (1993), 335-371.
20. J. Rogawski, The multiplicity formula for A-packets, Zeta functions of Picard modular surfaces (R. P. Langlands and D. Ramakrishnan, eds.), Publ. CRM, Montreal (1992), 395-418.
21. K. Rubin, Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer, Invent. Math. 64 (1981), 455-470.
22. J. Tate, Fourier analysis in number field and Hecke's Zeta functions, in: Algebraic number theory (Cassels and Frolich eds.), Academic Press, 1967.
23. J. Tate, Number theoretic background, Automorphic forms, representations and L-functions, Proc. Symp. pure math. 33-part 2 (1979), AMS Providence, 1-27.
24. F. Rodriguez Villegas, On the square root of special values of certain L-series, Invent. Math 106 (1991), 549-573.
25. F. Rodriguez Villegas, Square root formulas for central values of Hecke L-series II, Duke Math. J. 72 (1993), 431-440.
26. F. Rodriguez Villegas and Yonghai Yang, On the central special values of Hecke L-functions of CM number fields, Duke Math. J., to appear.
27. F. R. Villegas and D. Zagier, Square roots of central values of Hecke L-series, in: Proceeding of the 3rd conference of Canadian number theory association, Kingston, Ontario, 1991.
28. N. Wallach, Symplectic geometry and Fourier Analysis, Math. Sci. Press, 1977.
29. L. Washington, Introduction to Cyclotomic fields, Grad. Texts Math. 83, Springer-Verlag, 1982.
30. A. Weil, Sur la formule de Siegel dans la théorie des groupes classiques, Acta Math. 123 (1965), 1-87.
31. Tonghai Yang, Theta liftings and L-functions of elliptic curves, Ph.D. thesis, University of Maryland, College Park 1995.
32. Tonghai Yang, Nonvanishing of the central Hecke L-values and rank of Gross's elliptic curves, Comp. Math. (1996), submitted.
33. Tonghai Yang, Common zeros of theta functions and central Hecke L-values of CM number fields of degree 4, Proc. AMS., to appear.
34. Tonghai Yang, Eigenfunctions of Weil representations of unitary groups of one variable, Trans. AMS. (1995), to appear.