On the quotient sequence of sequences of integers

• Autorzy: Rudolf Ahlswede , Levon H. Khachatrian , András Sárközy
• Języki publikacji: EN

Kategorie tematyczne

• 11N25: Distribution of integers with specified multiplicative constraints

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 91
• Numer: 2
• Strony: 117-132

Daty

wydano

1999

otrzymano

1998-09-18

poprawiono

1999-05-24

Twórcy

autor

Rudolf Ahlswede

• Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

autor

Levon H. Khachatrian

• Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany

autor

András Sárközy

• Department of Algebra and Number Theory, Eötvös University, Múzeum krt. 6-8, H-1088 Budapest, Hungary

Bibliografia

• [1] R. Ahlswede and L. H. Khachatrian, Classical results on primitive and recent results on cross-primitive sequences, in: The Mathematics of Paul Erdős, Vol. I, R. L. Graham and J. Nešetřil (eds.), Algorithms Combin. 13, Springer, 1997, 104-116.
• [2] F. Behrend, On sequences of numbers not divisible by one another, J. London Math. Soc. 10 (1935), 42-44.
• [3] H. Davenport and P. Erdős, On sequences of positive integers, Acta Arith. 2 (1936), 147-151.
• [4] P. Erdős, Note on sequences of integers no one of which is divisible by any other, J. London Math. Soc. 10 (1935), 126-128.
• [5] P. Erdős, A generalization of a theorem of Besicovitch, J. London Math. Soc. 11 (1936), 92-98.
• [6] P. Erdős, On the distribution of additive functions, Ann. of Math. 97 (1946), 1-20.
• [7] P. Erdős, A. Sárközy and E. Szemerédi, On the divisibility properties of sequences of integers I, Acta Arith. 11 (1966), 411-418.
• [8] P. Erdős, A. Sárközy and E. Szemerédi, On divisibility properties of sequences of integers, in: Colloq. Math. Soc. János Bolyai 2, 1970, 35-49.
• [9] H. Halberstam and K. F. Roth, Sequences, Springer, Berlin, 1983.
• [10] G. H. Hardy and S. Ramanujan, The normal number of prime factors of a number n, Quart. J. Math. 48 (1920), 76-92.
• [11] J. Kubilius, Probabilistic Methods in the Theory of Numbers, Amer. Math. Soc. Transl. Math. Monographs 11, Providence, 1964.
• [12] C. Pomerance and A. Sárközy, On homogeneous multiplicative hybrid problems in number theory, Acta Arith. 49 (1988), 291-302.
• [13] A. Sárközy, On divisibility properties of sequences of integers, in: The Mathematics of Paul Erdős, Vol. I, R. L. Graham and J. Nešetřil (eds.), Algorithms Combin. 13, Springer, 1997, 241-250.
• [14] L. G. Sathe, On a problem of Hardy on the distribution of integers having given number of prime factors, J. Indian Math. Soc. 17 (1953), 63-141; and 18 (1954), 27-81.
• [15] A. Selberg, Note on a paper by L. G. Sathe, J. Indian Math. Soc. 18 (1954), 83-87.