Primes generated by elliptic curves
نویسندگان
چکیده
منابع مشابه
The Splitting of Primes in Division Fields of Elliptic Curves
Given a Galois extension L/K of number fields with Galois group G, a fundamental problem is to describe the (unramified) primes p of K whose Frobenius automorphisms lie in a given conjugacy class C of G. In particular, all such primes have the same splitting type in a sub-extension of L/K. In general, all that is known is that the primes have density |C|/|G| in the set of all primes, this being...
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At a prime of ordinary reduction, the Iwasawa “main conjecture” for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the p-adic L-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is ...
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The main question addressed in this paper focuses on the frequency with which the reductions modulo primes of a rational elliptic curve give rise to cyclic groups. This question is part of a broad theme of investigations about the distribution of Frobenius in an infinite family of division fields defined by an elliptic curve over a global field (or in variations of such families in other arithm...
متن کاملThe anticyclotomic Main Conjecture for elliptic curves at supersingular primes
The Main Conjecture of Iwasawa theory for an elliptic curve E over Q and the anticyclotomic Zp-extension of an imaginary quadratic field K was studied in [BD2], in the case where p is a prime of ordinary reduction for E. Analogous results are formulated, and proved, in the case where p is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by...
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will contain infinitely many prime terms — known as Mersenne primes. The Mersenne prime conjecture is related to a classical problem in number theory concerning perfect numbers. A whole number is said to be perfect if, like 6 = 1 + 2 + 3 and 28 = 1 + 2 + 4 + 7 + 14, it is equal to the sum of all its divisors apart from itself. Euclid pointed out that 2k−1(2k − 1) is perfect whenever 2 − 1 is pr...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2003
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-03-07311-8