Non-vanishing of -th derivatives of twisted elliptic -functions in the critical point
Journal de théorie des nombres de Bordeaux (1997)
- Volume: 9, Issue: 1, page 1-10
- ISSN: 1246-7405
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topPomykała, Jacek. "Non-vanishing of $n$-th derivatives of twisted elliptic $L$-functions in the critical point." Journal de théorie des nombres de Bordeaux 9.1 (1997): 1-10. <http://eudml.org/doc/248001>.
@article{Pomykała1997,
abstract = {Let $E$ be a modular elliptic curve over $\mathbb \{Q\}$$L^\{(n)\}(s, E)$ denote the $n$-th derivative of its Hasse-Weil $L$-series. We estimate the number of twisted elliptic curves $E_d, d \le D$ such that $L^\{(n)\} (1, E_d) \ne 0$.},
author = {Pomykała, Jacek},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {non-vanishing; -th derivatives; twisted elliptic -functions; twist; modular elliptic curve; zeta function},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Université Bordeaux I},
title = {Non-vanishing of $n$-th derivatives of twisted elliptic $L$-functions in the critical point},
url = {http://eudml.org/doc/248001},
volume = {9},
year = {1997},
}
TY - JOUR
AU - Pomykała, Jacek
TI - Non-vanishing of $n$-th derivatives of twisted elliptic $L$-functions in the critical point
JO - Journal de théorie des nombres de Bordeaux
PY - 1997
PB - Université Bordeaux I
VL - 9
IS - 1
SP - 1
EP - 10
AB - Let $E$ be a modular elliptic curve over $\mathbb {Q}$$L^{(n)}(s, E)$ denote the $n$-th derivative of its Hasse-Weil $L$-series. We estimate the number of twisted elliptic curves $E_d, d \le D$ such that $L^{(n)} (1, E_d) \ne 0$.
LA - eng
KW - non-vanishing; -th derivatives; twisted elliptic -functions; twist; modular elliptic curve; zeta function
UR - http://eudml.org/doc/248001
ER -
References
top- [B-S] B. Birch and H. Swinnerton-Dyer, Elliptic curves and modular functions, in Modular functions of one variable IV, Lecture Notes in Mathematics, Springer-Verlag, vol. 476, 1975, pp. 2-32. Zbl1214.11081MR384813
- [B-F-H] D. Bump, S. Friedberg and H. Hoffstein, Non-vanishing theorems for L- functions of modular forms and their derivatives, Invent. Math.102 (1990), 543-618. Zbl0721.11023MR1074487
- [HB] D.R. Heath-Brown, A mean value estimate for real character sum, Acta Arith.72 (1995), 235-275. Zbl0828.11040MR1347489
- [Iw] H. Iwaniec, On the order of vanishing of modular L-functions at the critical point, Séminaire de Théorie des Nombres de Bordeaux2 (1990), 365-376. Zbl0719.11029MR1081731
- [M-M] M.R. Murty and V.K. Murty, Mean values of derivatives of modular L-series, Ann. of Math.133 (1991), 447-475. Zbl0745.11032MR1109350
- [Mo] H.L. Montgomery, Topics in Multiplicative Number Theory, Lecture notes in Mathematics, Springer-Verlag, vol. 227, 1971. Zbl0216.03501MR337847
- [Ko] V.A. Kolyvagin, Finiteness of E(Q) and III(E(Q)) for a subclass of Weil curves, Math. USSR Izvest.32 (1989), 523-542. Zbl0662.14017MR954295
- [P-P] A. Perelli and J. Pomykala, Averages over twisted elliptic L-functions, Acta Arith.80 (1997), 149-163. Zbl0878.11022MR1450922
- [P-S] J. Pomykala and J. Szmidt, On the order of vanishing of n-th derivatives of L-functions of elliptic curves, Biuletyn Wojskowej Akademii Technicznej1242/496 (1993).
- [Wa] J.-L. Waldspurger, Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl.60 (1981), 375-484. Zbl0431.10015MR646366
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