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James Parks
- Int. J. Number Theory

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...cture 1.1. (iii) We remark that for 1 ≤ i ≤ L− 1, we have that p−i := pi + 1− 2 √ pi < pi+1 := #Epi(Fpi) < p + i := pi + 1 + 2 √ pi (1.1) by Hasse’s Theorem (see [Sil, Chapter V, Theorem 1.1]). Jones =-=[Jon]-=- refined Conjecture 1.1 in the non-CM case. He gave a precise conjectural constant CE,L in the asymptotic formula for πE,L(X). This formula was obtained by using a probabilistic model which adjusted t...

by
James Parks

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... for its behavior in the non-CM case. The main focus of their work was on aliquot cycles in the CM-case, where they proved that there are only finitely many under certain conditions when L ≥ 3. Jones =-=[Jon]-=- refined Conjecture 1.1 in the non-CM case for aliquot cycles by using a heuristic argument similar to that of Lang and Trotter [LaTr]. We state the refined conjecture in the particular case of amicab...

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