Skip to main content
SpringerLink
Log in

András Sárközy – a retrospective on the occasion of his sixtieth birthday

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  1. S. Ahlgren, Distribution of parity in the partition function on arithmetic progressions, Indag. Math. 10 (1999), 173–181.

    Google Scholar 

  2. R. Ahlswede, L. H. Khachatrian and A. SÁrkÖzy, On the counting function of primitive sets of integers, J. Number Theory 79 (1999), 330–344.

    Google Scholar 

  3. R. Ahlswede, L. H. Khachatrian and A. SÁrkÖzy, On the quotient sequence of sequences of integers, Acta Arith. 91 (1999), 117–132.

    Google Scholar 

  4. R. Balasubramanian, A note on a result of Erdős, Sárközy and Sós, Acta Arith. 49 (1987), 45–53.

    Google Scholar 

  5. A. Balog and A. SÁrkÖzy, On sums of integers having small prime factors, I., Studia Sci. Math. Hungar. 19 (1984), 35–47.

    Google Scholar 

  6. A. Balog and A. SÁrkÖzy, On sums of integers having small prime factors, II., Studia Sci. Math. Hungar. 19 (1984), 81–89.

    Google Scholar 

  7. A. Balog and A. SÁrkÖzy, On sums of sequences of integers, II., Acta Math. Acad. Sci. Hungar. 44 (1984), 169–179.

    Google Scholar 

  8. A. Balog and A. SÁrkÖzy, On sums of sequences of integers, III., Acta Math. Acad. Sci. Hungar. 44 (1984), 339–349.

    Google Scholar 

  9. J. Beck, Roth's estimate on the discrepancy of integer sequences is nearly sharp, Combinatorica 1 (1981), 319–325.

    Google Scholar 

  10. J. Beck, A. SÁrkÖzy and C. L. Stewart, On irregularities of distribution in shifts and dilations of integer sequences, II., in: Number Theory in Progress, Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in honor of the 60th birthday of Andrzej Schinzel, Zakopane, Poland, June 30–July 9, 1997, eds. K. Győry et al., Walter de Gruyter, Berlin-New York, 1999; 633–638.

    Google Scholar 

  11. F. Behrend, On sequences of integers not divisible one by another, J. London Math. Soc. 10 (1935), 42–44.

    Google Scholar 

  12. Y. Bugeaud, On the greatest prime factor of (ab+1)(bc+1)(ca+1); Acta Arith. 86 (1998), 45–49.

    Google Scholar 

  13. J. Cassaigne, S. Ferenczi, C. Mauduit, J. Rivat and A. SÁrkÖzy, On finite pseudorandom binary sequences, III. (The Liouville function, I.), Acta Arith. 87 (1999), 367–390.

    Google Scholar 

  14. Á. Elbert and A. SÁrkÖzy, Über rationale Polynome, Annales Univ. Sci. Budapest Eötvös 5 (1962), 155–171.

    Google Scholar 

  15. P. D. T. A. Elliott and A. SÁrkÖzy, The distribution of the number of prime divisors of sums a + b; J. Number Theory 29 (1988), 94–99.

    Google Scholar 

  16. P. ErdŐs, H. Maier and A. SÁrkÖzy, On the distribution of the number of prime factors of sums a + b; Trans. Amer. Math. Soc. 302 (1987), 269–280.

    Google Scholar 

  17. P. ErdŐŐs, C. Pomerance, A. SÁrkÖzy and C. L. Stewart, On elements of sumsets with many prime factors, J. Number Theory 44 (1993), 93–104.

    Google Scholar 

  18. P. ErdŐs and A. SÁrkÖzy, On the divisibility properties of sequences of integers, Proc. London Math. Soc. 21 (1970), 97–101.

    Google Scholar 

  19. P. ErdŐs and A. SÁrkÖzy, Problems and results on additive properties of general sequences, I., Pacific J. Math. 118 (1985), 347–357.

    Google Scholar 

  20. P. ErdŐs and A. SÁrkÖzy, Problems and results on additive properties of general sequences, II., Acta Math. Acad. Sci. Hungar. 48 (1986), 201–211.

    Google Scholar 

  21. P. ErdŐs, A. SÁrkÖzy and V. T. SÓs, Problems and results on additive properties of general sequences, IV., in: Number Theory, Proceedings, Ootacamund, India, 1984, ed. K. Alladi, Lecture Notes in Mathematics 1122, Springer-Verlag, Berlin–Heidelberg–New York, 1985; 85–104.

    Google Scholar 

  22. P. ErdŐs, A. SÁrkÖzy and V. T. SÓs, Problems and results on additive properties of general sequences, V., Monatshefte Math. 102 (1986), 183–197.

    Google Scholar 

  23. P. ErdŐs, A. SÁrkÖzy and V. T. SÓs, Problems and results on additive properties of general sequences, III., Studia Sci. Math. Hungar. 22 (1987), 53–63.

    Google Scholar 

  24. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, On divisibility properties of sequences of integers, Studia Sci. Math. Hungar. 1 (1966), 431–435.

    Google Scholar 

  25. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, On the divisibility properties of sequences of integers, I., Acta Arith. 11 (1966), 411–418.

    Google Scholar 

  26. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, On the solvability of the equations [a i; aj] = a r and (a ′i ,a ′j ) = a ′r in sequences of positive density, J. Math. Anal. Appl. 15 (1966), 60–64.

    Google Scholar 

  27. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, On a theorem of Behrend, J. Australian Math. Soc. 7 (1967), 9–16.

    Google Scholar 

  28. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, On an extremal problem concerning primitive sequences, J. London Math. Soc. 42 (1967), 484–488.

    Google Scholar 

  29. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, The solvability of certain equations in dense sequences of integers (in Russian), Dokl. Akad. Nauk SSSR 176 (1967), 541–544.

    Google Scholar 

  30. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, On the divisibility properties of sequences of integers, II., Acta Arith. 14 (1968), 1–12.

    Google Scholar 

  31. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, On the solvability of certain equations in sequences of positive upper logarithmic density, J. London Math. Soc. 43 (1968), 71–78.

    Google Scholar 

  32. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, Über Folgen ganzer Zahlen, in: Abhandlungen aus Zahlentheorie und Analysis (zur Errinnerung an E. Landau), Plenum, New York, 1969; 77–86.

    Google Scholar 

  33. P. ErdŐs, A. SÁrkÖzy and E. SzemerÉdi, On divisibility properties of sequences of integers, Coll. Math. Soc. J. Bolyai 2 (Number Theory, Debrecen, 1968) (1970), 35–49.

    Google Scholar 

  34. P. ErdŐs, C. L. Stewart and R. Tijdeman, Some Diophantine equations with many solutions, Compositio Math. 66 (1988), 37–56.

    Google Scholar 

  35. A. Fujii, An additive problem in theory of numbers, Acta Arith. 40 (1981), 41–49.

    Google Scholar 

  36. H. Furstenberg, Ergodic behaviour of diagonal measures and a theorem of Szemerédi on arithmetic progressions, J. d'Analyse Math. 31 (1977), 204–256.

    Google Scholar 

  37. K. GyŐry and A. SÁrkÖzy, On prime factors of integers of the form (ab+ 1)(bc + 1)(ca + 1); Acta Arith. 79 (1997), 163–171.

    Google Scholar 

  38. K. GyŐry, A. SÁrkÖzy and C. L. Stewart, On the number of prime factors of integers of form ab+ 1; Acta Arith. 74 (1996), 365–385.

    Google Scholar 

  39. H. Iwaniec and A. SÁrkÖzy, On a multiplicative hybrid problem, J. Number Theory 26 (1987), 89–95.

    Google Scholar 

  40. T. Kamae and M. MendÉs-France, Van der Corput's diffrence theorem, Israel J. Math. 31 (1978), 335–342.

    Google Scholar 

  41. O. Kolberg, Note on the parity of the partition function, Math. Scand. 7 (1959), 377–378.

    Google Scholar 

  42. L. LovÁsz, A. SÁrkÖzy and M. Simonovits, On additive arithmetic functions satisfying a linear recursion, Annales Univ. Sci. Budapest Eötvös 24 (1981), 205–215.

    Google Scholar 

  43. P. A. MacMahon, Note on the parity of the number which enumerates the partitions of a number, Proc. Cambridge Phil. Soc. 20 (1921), 281–283.

    Google Scholar 

  44. P. A. MacMahon, The parity of p(n); the number of partitions of n; when n ≤ 1000; J. London Math. Soc. 1 (1926), 225–226.

    Google Scholar 

  45. J. MatouŠek and J. Spencer, Discrepancy in arithmetic progressions, J. Amer. Math. Soc. 9 (1996), 195–204.

    Google Scholar 

  46. C. Mauduit and A. SÁrkÖzy, On finite pseudorandom binary sequences, I. Measure of pseudorandomness, the Legendre symbol, Acta Arith. 82 (1997), 365–377.

    Google Scholar 

  47. C. Mauduit and A. SÁrkÖzy, On finite pseudorandom binary sequences, II. (The Champernowne, Rudin–Shapiro and Thue–Morse sequences. A further construction.), J. Number Theory 73 (1998), 256–276.

    Google Scholar 

  48. L. Mirsky, The distribution of the partition function in residue classes, J. Math. Anal. Appl. 93 (1983), 593–598.

    Google Scholar 

  49. J.-L. Nicolas, I. Z. Ruzsa and A. SÁrkÖzy, On the parity of additive representation functions, J. Number Theory 73 (1998), 292–317.

    Google Scholar 

  50. J.-L. Nicolas and A. SÁrkÖzy, On the parity of partition functions, Illinois J. Math. 39 (1995), 586–597.

    Google Scholar 

  51. K. Ono, Parity of the partition function in arithmetic progressions, J. Reine Angew. Math. 472 (1996), 1–15.

    Google Scholar 

  52. K. Ono, Distribution of the partition function modulo m, Ann. Math. 151 (2000), 293–307.

    Google Scholar 

  53. J. Pintz, W. L. Steiger and E. SzemerÉdi, On sets of natural numbers whose diffrence set contains no squares, J. London Math. Soc. 37 (1988), 219–231.

    Google Scholar 

  54. C. Pomerance and A. SÁrkÖzy, On homogeneous multiplicative hybrid problems in number theory, Acta Arith. 49 (1988), 291–302.

    Google Scholar 

  55. K. F. Roth, Remark concerning integer sequences, Acta Arith. 9 (1964), 257–260.

    Google Scholar 

  56. I. Ruzsa, Large prime factors of sums, Studia Sci. Math. Hungar. 27 (1992), 463–470.

    Google Scholar 

  57. A. SÁrkÖzy, Some remarks concerning irregularities of distribution of sequences of integers in arithmetic progressions, I., Coll. Math. Soc. J. Bolyai 13 (Topics in Number Theory, Debrecen) (1974), 287–303.

    Google Scholar 

  58. A. SÁrkÖzy, Some remarks concerning irregularities of distribution of sequences of integers in arithmetic progressions, II., Studia Sci. Math. Hungar. 11 (1976), 79–103.

    Google Scholar 

  59. A. SÁrkÖzy, Some remarks concerning irregularities of distribution of sequences of integers in arithmetic progressions, IV., Acta Math. Acad. Sci. Hungar. 30 (1977), 155–162.

    Google Scholar 

  60. A. SÁrkÖzy, On diffrence sets of sequences of integers, I., Acta Math. Acad. Sci. Hungar. 31 (1978), 125–149.

    Google Scholar 

  61. A. SÁrkÖzy, On diffrence sets of sequences of integers, III., Acta Math. Acad. Sci. Hungar. 31 (1978), 355–386.

    Google Scholar 

  62. A. SÁrkÖzy, On multiplicative arithmetic functions satisfying a linear recursion, Studia Sci. Math. Hungar. 13 (1978), 79–104.

    Google Scholar 

  63. A. SÁrkÖzy, Some remarks concerning irregularities of distribution of sequences of integers in arithmetic progressions, III., Periodica Math. Hungar. 9 (1978), 127–144.

    Google Scholar 

  64. A. SÁrkÖzy, On sums a+b and numbers of the form ab+1 with many prime factors, Grazer Math. Ber. 318 (1992), 141–154.

    Google Scholar 

  65. A. SÁrkÖzy and C. L. Stewart, On divisors of sums of integers, II., J. Reine Angew. Math. 365 (1986), 171–191.

    Google Scholar 

  66. A. SÁrkÖzy and C. L. Stewart, On irregularities of distribution in shifts and dilations of integer sequences, I., Math. Annalen 276 (1987), 353–364.

    Google Scholar 

  67. A. SÁrkÖzy and C. L. Stewart, On divisors of sums of integers, IV., Canadian J. Math. 40 (1988), 788–816.

    Google Scholar 

  68. C. L. Stewart and R. Tijdeman, On the greatest prime factor of (ab + 1)(ac + 1)(bc + 1); Acta Arith. 79 (1997), 93–101.

    Google Scholar 

  69. G. Tenenbaum, Facteurs premiers de sommes d'entiers, Proc. Amer. Math. Soc. 106 (1989), 287–296.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    C. L. Stewart

Authors
  1. C. L. Stewart
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stewart, C.L. András Sárközy – a retrospective on the occasion of his sixtieth birthday. Periodica Mathematica Hungarica 42, 1–16 (2001). https://doi.org/10.1023/A:1015254221022

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015254221022

Keywords

Search

Navigation