A lower bound for the rank of J 0 ( q )

E. Kowalski; P. Michel

Acta Arithmetica (2000)

  • Volume: 94, Issue: 4, page 303-343
  • ISSN: 0065-1036

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Kowalski, E., and Michel, P.. "A lower bound for the rank of $J_0(q)$." Acta Arithmetica 94.4 (2000): 303-343. <http://eudml.org/doc/207433>.

@article{Kowalski2000,
author = {Kowalski, E., Michel, P.},
journal = {Acta Arithmetica},
keywords = {modular curves; modular forms; -functions; nonvanishing},
language = {eng},
number = {4},
pages = {303-343},
title = {A lower bound for the rank of $J_0(q)$},
url = {http://eudml.org/doc/207433},
volume = {94},
year = {2000},
}

TY - JOUR
AU - Kowalski, E.
AU - Michel, P.
TI - A lower bound for the rank of $J_0(q)$
JO - Acta Arithmetica
PY - 2000
VL - 94
IS - 4
SP - 303
EP - 343
LA - eng
KW - modular curves; modular forms; -functions; nonvanishing
UR - http://eudml.org/doc/207433
ER -

References

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  1. [CGG] J. B. Conrey, A. Ghosh and S. M. Gonek, Simple zeros of the Riemann zeta function, Proc. London Math. Soc. (3) 76 (1998), 497-522. Zbl0907.11025
  2. [Du] W. Duke, The critical order of vanishing of automorphic L-functions with high level, Invent. Math. 119 (1995), 165-174. Zbl0838.11035
  3. [DFI] W. Duke, J. Friedlander and H. Iwaniec, Bounds for automorphic L-functions, II, ibid. 115 (1994), 219-239. Zbl0812.11032
  4. [G-R] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed., Academic Press, 1994. Zbl0918.65002
  5. [GZ] B. Gross and D. Zagier, Heegner points and derivatives of L-series II, Math. Ann. 278 (1987), 497-562. Zbl0641.14013
  6. [Iw] H. Iwaniec, On the order of vanishing of modular L-functions at the critical point, Sém. Théor. Nombres Bordeaux 2 (1990), 365-376. Zbl0719.11029
  7. [ILS] H. Iwaniec, W. Luo and P. Sarnak, Low lying zeros for families of L-functions, preprint, 1998. 
  8. [IS] H. Iwaniec and P. Sarnak, The non-vanishing of central values of automorphic L-functions and Siegel's zeros, preprint, 1997. 
  9. [Jut] M. Jutila, Lectures on a Method in the Theory of Exponential Sums, Tata Lectures on Math. and Phys. 80, Springer, 1987. 
  10. [KS] N. Katz and P. Sarnak, Random Matrices, Frobenius Eigenvalues, and Monodromy, Amer. Math. Soc. Colloq. Publ. 45, 1999. Zbl0958.11004
  11. [Kow] E. Kowalski, The rank of the jacobian of modular curves: analytic methods, thesis, Rutgers University, May 1998 (available at http://www.princeton.edu/ekowalsk/These/these.html). 
  12. [KM1] E. Kowalski and P. Michel, The analytic rank of J 0 ( q ) and zeros of automorphic L-functions, Duke Math. J. 100 (1999), 503-542. Zbl1161.11359
  13. [KM2] E. Kowalski and P. Michel, Explicit upper bound for the rank of J 0 ( q ) , preprint, Université Montpellier II, 1998. 
  14. [Miy] T. Miyake, Modular Forms, Springer, 1989. 
  15. [Sh] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Iwanami Shoten and Princeton Univ. Press, 1971. Zbl0221.10029
  16. [Sou] K. Soundararajan, Non-vanishing of quadratic Dirichlet L-functions at s=1/2, preprint, 1999. 
  17. [VdK] J. VanderKam, The rank of quotients of J 0 ( N ) , preprint, 1997. 

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