Duke Mathematical Journal

Square root formulas for central values of Hecke $L$-series II

Fernando Rodriguez Villegas

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Article information

Source
Duke Math. J. Volume 72, Number 2 (1993), 431-440.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077289426

Digital Object Identifier
doi:10.1215/S0012-7094-93-07215-8

Mathematical Reviews number (MathSciNet)
MR1248679

Zentralblatt MATH identifier
0820.11036

Subjects
Primary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]

Citation

Villegas, Fernando Rodriguez. Square root formulas for central values of Hecke L -series II. Duke Math. J. 72 (1993), no. 2, 431--440. doi:10.1215/S0012-7094-93-07215-8. http://projecteuclid.org/euclid.dmj/1077289426.


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References

  • [1] R. Greenberg, On the Birch and Swinnerton-Dyer conjecture, Invent. Math. 72 (1983), no. 2, 241–265.
  • [2] B. Gross and D. Zagier, Heegner points and derivatives of $L$-series, Invent. Math. 84 (1986), no. 2, 225–320.
  • [3] B. Gross, Arithmetic on elliptic curves with complex multiplication, Lecture Notes in Mathematics, vol. 776, Springer, Berlin, 1980.
  • [4] F. Hirzebruch and D. Zagier, Intersection numbers of curves on Hilbert modular surfaces and modular forms of Nebentypus, Invent. Math. 36 (1976), 57–113.
  • [5] M. G. Humbert, Les fonctions abeliennes singulaires et les formes quadratiques, J. Math. 9 (1903), no. 5, 43–137.
  • [6] S. S. Kudla and J. J. Millson, The theta correspondence and harmonic forms. I, Math. Ann. 274 (1986), no. 3, 353–378.
  • [7] F. Rodriguez Villegas, On the square root of special values of certain $L$-series, Invent. Math. 106 (1991), no. 3, 549–573.
  • [8] F. Rodriguez Villegas and D. Zagier, Square roots of central values of $L$-series, to appear in Proceedings of the Third Conference of the Canadian Number Theory Association, Kingston, Ontario, 1991.
  • [9] D. Rohrlich, The nonvanishing of certain Hecke $L$-functions at the center of the critical strip, Duke Math. J. 47 (1980), no. 1, 223–232.
  • [10] G. Shimura, On modular forms of half integral weight, Ann. of Math. (2) 97 (1973), 440–481.
  • [11] G. Shimura, On the periods of modular forms, Math. Ann. 229 (1977), no. 3, 211–221.

See also

  • See also: Fernando Rodriguez Villegas, Don Zagier. Square roots of central values of Hecke L-series. Advances in number theory (Kingston, ON, 1991), pp. 81–99, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.