Average Frobenius distribution for the degree two primes of a number field
نویسندگان
چکیده
منابع مشابه
Average Frobenius Distribution for the Degree Two Primes of a Number Field
Let K be a number field and r an integer. Given an elliptic curve E, defined over K, we consider the problem of counting the number of degree two prime ideals of K with trace of Frobenius equal to r. Under certain restrictions on K, we show that “on average” the number of such prime ideals with norm less than or equal to x satisfies an asymptotic identity that is in accordance with standard heu...
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15 صفحه اولAverage Frobenius distribution for elliptic curves defined over finite
Let K be a fixed number field, assumed to be Galois over Q. Let r and f be fixed integers with f positive. Given an elliptic curve E , defined over K , we consider the problem of counting the number of degree f prime ideals of K with trace of Frobenius equal to r . Except in the case f = 2, we show that ‘on average,’ the number of such prime ideals with norm less than or equal to x satisfies an...
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Given an integer r, we consider the problem of enumerating the inert prime ideals p of Q(i) for which a given elliptic curve E has trace of Frobenius at p equal to r. We prove that on average the number of such prime ideals up to x is asymptotic to cr log log x where cr is an explicit constant computed in terms of an Euler product. This result is in accordance with the standard heuristics. This...
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2013
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004112000631