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S. Böcherer, R. Schulze-Pillot: The Dirichlet series of Koecher and Maass and modular forms of weight 3/2. Math. Z.209 (1992) 273–287
J.-M. Deshouillers, H. Iwaniec: Kloosterman sums and Fourier coefficients of cusp forms. Invent. Math.70 (1982) 219–288
W. Duke, J. Friedlander, H. Iwaniec: Bounds for automorphicL-functions. II. Invent. Math.115 (1994) 219–239
D. Goldfeld, J. Hoffstein, D. Lieman: An effective zero free region, Appendix to: Coefficeints of Maass forms and the Siegel zero Ann. Math. (to appear)
F. Gouvêa, B. Mazur: The square-free sieve and the rank of elliptic curves. J. AMS4 (1991) 1–23
B.H. Gross: Heights and the special values ofL-series. In: Number Theory, Proceedings of the 1985 Montreal Conference held June 17–29, 1985, CMS Conference Proceedings, Vol. 7, 1987, 115–187
J. Hoffstein, P. Lockhart: Coefficients of Maass forms and the Siegel zero. Ann. Math. (to appear)
H. Iwaniec: On the order of vanishing of modularL-functions at the critical point. In: Sém. Th. des Nombres, Bordeaux2 (1990) 365–376
W. Luo: On the nonvanishing of Rankin SelbergL-functions. Duke Math. J69 (1993) 411–427
B. Mazur: Modular curves and the Eisenstein ideal. IHES Publ. Math.47 (1977) 33–186
B. Mazur: On the arithmetic of special values ofL-functions. Invent. Math.55 (1979) 207–240
D.E. Rohrlich: OnL-functions of elliptic curves and cyclotomic towers. Invent. Math.75 (1984) 409–423
D.E. Rohrlich:L-functions and division towers. Math. Ann.281 (1988) 611–632
G. Shimura: Introduction to the arithmetic theory of automorphic functions. Publ. Math. Soc. Japan, Vol. 11. Tokyo-Princeton, 1971
Oblatum 19-IX-1993 & 2-V-1994
Research supported in part by NSF Grant DMS-9202022.
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Duke, W. The critical order of vanishing of automorphicL-functions with large level. Invent Math 119, 165–174 (1995). https://doi.org/10.1007/BF01245178
- Large Level
- Critical Order