Titlebook: Arithmetic on Modular Curves; Glenn Stevens Book 1982 Birkhäuser Boston 1982 algebra.arithmetic.function.number theory.proof

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https://doi.org/10.1007/978-1-4842-3742-7Mazur and Swinnerton-Dyer [30] have shown how to pass from a T.-eigenfunction on (ℚ/ℤ). to a p-adic distribution on ℤ.. Applying this procedure to the universal modular symbol on a modular curve, X, Mazur [26] defines a p-adic L-function L. (X.(N), χ, s) associated to an Eisenstein prime P for Г.(N), N prime.

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Background,We begin with a tour of the basic concepts which we will study in more detail in the following chapters. For our purposes the most important of these are the universal special value and the cuspidal group.

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0743-1643 t argument. Mazur‘s congruence formulae were extended to r 1 (N), N prime, by S. Kamienny and the author [17], and in a paper which will appear shortly, Kamienn978-0-8176-3088-1978-1-4684-9165-4Series ISSN 0743-1643 Series E-ISSN 2296-505X

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Book 1982gives information about the arithmetic of Xo (N). There are two aspects to his work: congruence formulae for the values Af(X) , and a descent argument. Mazur‘s congruence formulae were extended to r 1 (N), N prime, by S. Kamienny and the author [17], and in a paper which will appear shortly, Kamienn

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