منابع مشابه
On Primitive Points of Elliptic Curves with Complex Multiplication
Let E be an elliptic curve defined over Q and P ∈ E(Q) a rational point of infinite order. Suppose that E has complex multiplication by an order in the quadratic imaginary field k. Denote by ME,P the set of rational primes ` such that ` splits in k, E has good reduction at `, and P is a primitive point modulo `. Under the generalized Riemann hypothesis, we can determine the positivity of the de...
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Let E/K be an elliptic curve defined over a number field, and let P ∈ E(K) be a point of infinite order. It is natural to ask how many integers n ≥ 1 fail to occur as the order of P modulo a prime of K. For K = Q, E a quadratic twist of y2 = x3 − x, and P ∈ E(Q) as above, we show that there is at most one such n ≥ 3.
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(2) hn divides hm whenever n divides m. They have attracted number theoretical and combinatorial interest as some of the simplest nonlinear recurrence sequences (see [3] for references), but for us their interest lives in the underlying geometry: Ward demonstrates that an elliptic divisibility sequence arises from any choice of elliptic curve over Q and rational point on that curve. Theorem 1 (...
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We give a quantitative bound for the number of S-integral points on an elliptic curve over a number field K in terms of the number of primes dividing the denominator of the j-invariant, the degree [K : Q], and the number of primes in S. Let K be a number field of degree d and MK the set of places of K. Let E/K be an elliptic curve with quasi-minimal Weierstrass equation E : y = x +Ax+B. If ∆ = ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1977
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1977-14310-3