Browsing Waterloo Research by Subject "prime divisors"
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Number of prime factors with a given multiplicity
(Cambridge University Press, 2022-03)Let k ⩾ 1 be a natural number and ωk (n) denote the number of distinct prime factors of a natural number n with multiplicity k. We estimate the first and second moments of the functions ωk with k ⩾ 1. Moreover, we prove ... -
A prime analogue of the Erdös-Pomerance conjecture for elliptic curves
(European Mathematical Society, 2005-12-31)Let E/Q be an elliptic curve of rank ≥ 1 and b ∈ E(Q) a rational point of infinite order. For a prime p of good reduction, let gb(p) be the order of the cyclic group generated by the reduction b of b modulo p. We denote ... -
Prime analogues of the Erdős–Kac theorem for elliptic curves
(Elseiver, 2006-08)Let E/Q be an elliptic curve. For a prime p of good reduction, let E(Fp) be the set of rational points defined over the finite field Fp. We denote by ω(#E(Fp)), the number of distinct prime divisors of #E(Fp). We prove ...