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Additive Functions Monotonic on the Set of Primes II

Published online by Cambridge University Press:  20 November 2018

Jean-Marie De Koninck ,
Imre Kátai  and
Armel Mercier
Jean-Marie De Koninck
Affiliation:
Département de mathématiques et statistique, Université Laval, Québec, QuébecG1K 7P4
Imre Kátai
Affiliation:
Eötvös Loránd University, Computer Center, 1117 Budapest, Bogdánfy u. 10/B, Hungary, Ontario L8S 4K1
Armel Mercier
Affiliation:
Département de mathématiques, Université du Québec, Chicoutimi, Québec G7H 2B1
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Let L: [1, ∞) → [1, ∞) be a nondecreasing function such that limx→∞L(x) = +∞. Let f= fL be a strongly additive function determined by f(p) = L(p) on the set of primes. In what followsp, p1, p2, …, q, q1, q2, …,P, Q stand for prime numbers, P(n) denotes the largest prime divisor of n. The letters c, c1, c2, … denote suitable positive constants, not necessarily the same at each occurrence. As usual, π(x) denotes the number of primes p ≤ x, while π(x, k, ℓ) is the number of primes p ≤ x such that p ≡ ℓ (mod k).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 4 , 01 August 1991 , pp. 705 - 720
Copyright
Copyright © Canadian Mathematical Society 1991

References

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