On the order of vanishing of modular -functions at the critical point

Henryk Iwaniec

Journal de théorie des nombres de Bordeaux (1990)

  • Volume: 2, Issue: 2, page 365-376
  • ISSN: 1246-7405

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Iwaniec, Henryk. "On the order of vanishing of modular $L$-functions at the critical point." Journal de théorie des nombres de Bordeaux 2.2 (1990): 365-376. <http://eudml.org/doc/93522>.

@article{Iwaniec1990,
author = {Iwaniec, Henryk},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {twisted L-function; vanishing theorem; cusp form; elliptic curve; integral representation for the L-series; symmetric square L-series; large sieve inequality},
language = {eng},
number = {2},
pages = {365-376},
publisher = {Université Bordeaux I},
title = {On the order of vanishing of modular $L$-functions at the critical point},
url = {http://eudml.org/doc/93522},
volume = {2},
year = {1990},
}

TY - JOUR
AU - Iwaniec, Henryk
TI - On the order of vanishing of modular $L$-functions at the critical point
JO - Journal de théorie des nombres de Bordeaux
PY - 1990
PB - Université Bordeaux I
VL - 2
IS - 2
SP - 365
EP - 376
LA - eng
KW - twisted L-function; vanishing theorem; cusp form; elliptic curve; integral representation for the L-series; symmetric square L-series; large sieve inequality
UR - http://eudml.org/doc/93522
ER -

References

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  1. [1] E. Bombieri, Le grand Crible dans la Théorie Analytique des Nombres, Astérique18 (1973). Zbl0292.10035MR371840
  2. [2] D. Bump, S. Friedberg and J. Hoffstein, Eisenstein series on the metaplectic group and non-vanishing theorems for automorphic L-functions and their derivatives. Ann. Math.131 (1990), 53-127. Zbl0699.10039MR1038358
  3. [3] J.-M. Deshouillers and H. Iwaniec, The non-vanishing of Rankin-Selberg zeta-functions at special points, AMS Contemporary Mathematics Vol.53 (1986), 51-95. Zbl0595.10025MR853553
  4. [4] V.A. Kolyvagin, Finateness of E(Q) and III(E, Q) for a subclass of Weil curves. Math. USSR Izv. Zbl0662.14017
  5. [5] K. Murty and R. Murty, Mean values of derivatives of modular L-series. (to appear in Ann. Math.). (See also K. Murty, Non-vanishing of L-functions and their derivatives in Automorphic Forms and Analytic Number Theory, (edited by R. Murty), CRM Publications, Montreal1990, 89-113). Zbl0745.11033
  6. [6] R.S. Phillips and P. Sarnak, On cusp forms for co-finite subgroups of PSL(2, R). Invent. Math.80 (1985), 339-364. Zbl0558.10017MR788414
  7. [7] D. Rohrlich, On L-functions of elliptic curves and anticyclotomic towers. Invent. Math.75 (1984), 383-408. Zbl0565.14008MR735332
  8. [8] D. Rohrlich, On L-functions of elliptic curves and cyclotomic towers. Invent. Math.75 (1984), 409-423. Zbl0565.14006MR735333
  9. [9] D. Roiirlich, L-functions and division towers. Math. Ann.281(1988), 611-632. Zbl0656.14013MR958262
  10. [10] D. Rohrlich, Non-vanishing of L-functions for GL(2). Invent. Math.97 (1989), 381-403. Zbl0677.10020
  11. [11] D. Rohrlich, The vanishing of certain Rankin-Selberg convolutions, in Automorphic Forms and Analytic Number Theory. (edited by R. Murty) CRM Publications, Montreal1990, 123-133. Zbl0737.11014MR1111015
  12. [12] G. Shimura, On modular forms of half-integral weight. Ann. Math.97 (1973), 440-481. Zbl0266.10022MR332663

Citations in EuDML Documents

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  1. Guillaume Ricotta, Nicolas Templier, Comportement asympotique des hauteurs des points de Heegner
  2. Jacek Pomykała, Non-vanishing of -th derivatives of twisted elliptic -functions in the critical point
  3. E. Kowalski, P. Michel, A lower bound for the rank of
  4. A. Perelli, J. Pomykała, Averages of twisted elliptic L-functions

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