Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-15T19:38:59.161Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. de Bruijn, N.G., On the number of positive integers ≤ x and free of prime factors > y, Koninkl. Nederl. Akademie Van Wetenschappen, Series A 54(1951), 49–60.+y,+Koninkl.+Nederl.+Akademie+Van+Wetenschappen,+Series+A+54(1951),+49–60.>Google Scholar
2. De Koninck, J.M., Kátai, I., Mercier, A., Additive functions monotonie on the set of primes, Acta Arith. 57(1991),41–68.Google Scholar
3. Erdös, P. and Pomerance, C., On the largest prime factors of n and n, + 1, Aequationes Math. 17(1978), 311–321.Google Scholar
4. Erdös, P., Some remarks on prime factors of integers, Can. J. Math. 11(1959), 161–167.Google Scholar
5. Halberstam, H. and Richert, H.E., Sieve Methods. L.M.S. Monograph, Academic Press, 1975.Google Scholar
6. Perelli, A., Pintz, J. and Salerno, S., BombierVs theorem in short intervals II, Invent. Math. 79(1985), 1–9.Google Scholar
7. Turan, P., On a theorem of Hardy and Ramanujan, J. London Math. Soc. 9(1934), 274–276.Google Scholar
8. Ward, D.R., Some series involving Euler's function, J. London Math. Soc. 2(1927), 210–214.Google Scholar