Counting Squarefree Discriminants of Trinomials under Abc Anirban Mukhopadhyay, M. Ram Murty and Kotyada Srinivas
نویسنده
چکیده
where Z denotes the set of integers. For positive integers A > 1, B > 1 we defineMn(A,B) to be the set of (a, b) with A ≤ |a| ≤ 2A, B ≤ |b| ≤ 2B such that f(t) is irreducible and Df is squarefree. It is reasonable to expect that for A, B tending to infinity, Mn(A,B) ∼ cnAB, for some positive constant cn. This is probably very difficult to prove. We will apply the abc conjecture to show that Mn(A,B) ≫ AB. Recall that the abc-conjecture, first formulated in 1985 by Oesterlé and Masser is the following statement. Fix ǫ > 0. If a, b and c are coprime positive integers satisfying a+ b = c, then c ≪ǫ N(a, b, c) where N(a, b, c) is the product of dictinct primes dividing abc.
منابع مشابه
Counting Squarefree Discriminants of Trinomials under Abc
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