1972
DOI: 10.1070/im1972v006n01abeh001867
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Parabolic Points and Zeta-Functions of Modular Curves

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Cited by 206 publications
(75 citation statements)
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“…Since the element c% in the Iwasawa algebra A is uniquely determined by the integrals L(E,)O where Z ranges through all characters of finite order with values in extensions of D (see the proposition of (7.6)), we may take the formulae of (9.6) and (9.7) as uniquely characterizing the p-adic L-series of E. These formulae give at the same time the relationship between the various p-adic L-series, for different p, and the complex L-series of the Weil curve E [10,12]. is equivalent to the assertion that an expression of the form…”
Section: (82) Volumes Associated To Eigenfunetionsmentioning
confidence: 97%
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“…Since the element c% in the Iwasawa algebra A is uniquely determined by the integrals L(E,)O where Z ranges through all characters of finite order with values in extensions of D (see the proposition of (7.6)), we may take the formulae of (9.6) and (9.7) as uniquely characterizing the p-adic L-series of E. These formulae give at the same time the relationship between the various p-adic L-series, for different p, and the complex L-series of the Weil curve E [10,12]. is equivalent to the assertion that an expression of the form…”
Section: (82) Volumes Associated To Eigenfunetionsmentioning
confidence: 97%
“…If ~p: Xo(N)~E is a weak Weil parametrization, and ~Xo(N) is a cusp, it is a theorem of Manin [10,12] that (p(a) is a point of finite order in E. For the cusp a =0, one has more precise information. For example, a recent calculation of Ogg [15] (the theorem of w 3) assures us that the divisor (0)-(i~) in the Jacobian of Xo(N), for N a prime number, is of order precisely the numerator of (N-1)/12.…”
Section: H+_~zmentioning
confidence: 98%
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“…of what is usually referred to as a Manin symbol [Man72] (i.e., that associated to the pair (a, b)). It is independent of the choices of a, b, c, and d. We will often abuse notation and refer to [u : v] r for integers u and v with (u, v, N p) = 1.…”
mentioning
confidence: 99%