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J. P. L. Knopfmacher - Publication List up to March 2002

Books/ Monographs

  1. - North-Holland/American Elsevier Publishing Co.. (Amsterdam/New York, 1975); Second Edition - Dover Publications Inc. (New York, 1990).
  2. - M. Dekker Inc., (New York/Basel, 1979).
  3. , Dekker, 2001.

Posthumous Additions

  • "Abstract Analytic Number Theory", in Encyclopaedia of Mathematics Supplement III, Kluwer Academic Pub.,(2001),13-17.
  • "Abstract Prime Number Theory", in Encyclopaedia of Mathematics Supplement III, Kluwer Academic Pub.,(2001),17-19.
  • "Recent developments and applications of abstract analytic number theory", Quaestiones Mathematicae, 24 (2001),291-308.
  • "Arithmetical semigroups related to trees and polyhedra, II" (with Richard Warlimont, Germany), Math. Nachr. 235 (2002), 59-81.

Refereed papers as sole author

  1. "Note on perfect numbers", Math Gazette, 44 (1960), 45.
  2. "Universal envelopes for non-associative algebras", Quart. J. Math. (Oxford), 13 (1962), 264-282.
  3. "On Chern classes of representations of finite groups", Bulletin American Math. Soc., 71 (1965), 568-571.
  4. "Extensions in varieties of groups and algebras", Acta Mathematica (Sweden), 115 (1966), 17-50.
  5. "Homology and presentations of algebras", Proc. American Math. Soc., 17 (1966), 1424-1428.
  6. "On Chern classes of representations of finite groups", J. London Math. Soc., 41 (1967), 535-541.
  7. "On the isomorphism problem for Lie algebras", Proc. American Math. Soc., 18 (1967), 898-901.
  8. "Some homological formulae", J. Algebra, 9 (1968), 212-219.
  9. "Note on finite topological spaces", J. Australian Math. Soc., 9 (1969), 252-256.
  10. "On Lie algebra obstructions", Bulletin Australian Math. Soc., 1 (1969), 281-288.
  11. "Arithmetical properties of finite rings and algebras, and analytic number theory", Bulletin American Math. Soc., 76 (1970),830-833.
  12. "Asymptotic enumeration of manifolds and Lie groups", Mathematische Annalen, 190 (1970), 129-134.
  13. "Arithmetical properties of finite rings and algebras, and analytic number theory", J. f?r die reine und angew. Math., 252 (1972), 16-43.
  14. "Finite modules and algebras over Dedekind domains and analytic number theory", Bulletin American Math. Soc., 78 (1972), 193-196.
  15. "Arithmetical properties of finite rings and algebras, and analytic number theory, II : Categories and analytic number theory", J. f?r die reine und angew. Math., 254 (1972) , 74-99.
  16. "Arithmetical properties of finite rings and algebras, and analytic number theory, III :Finite modules and algebras over Dedekind domains", J. f?r die reine und angew. Math., 259 (1973), 157-170.
  17. "A prime-divisor function", Proc. American Math. Soc., 40 (1973), 373-377.
  18. Arithmetical properties of finite rings and algebras, and analytic number theory, IV : Relative asymptotic enumeration and L-series", J. f?r die reine und angew. Math., 270 (1974) 97-114.
  19. "Arithmetical properties of finite rings and algebras, and analytic number theory, V : Categories and relative analytic number theory", J. f?r die reine und angew. Math., 271(1974), 95-121.
  20. "On measures of fuzziness", J. Math. Analysis & Appl., 49 (1975),529-534.
  21. "Arithmetical properties of finite rings and algebras, and analytic number theory, VI : Maximum orders of magnitude", J f?r die reine und angew. Math., 277 (1975), 45-62.
  22. "On the asymptotic enumeration of finite rings and modules", Archiv der Math., 26 (1975), 615-619.
  23. "Fourier analysis of arithmetical functions", Annali di Mat. Pura ed Appl., 109 (1976),177-201.
  24. "Arithmetical properties of finite graphs and polynomials", J. Combinatorial Theory, Series B,20 (1976), 205-215.
  25. "Finite modules and algebras over rings of algebraic functions", Bulletin London Math. Soc., 8 (1976), 289-293.
  26. "An abstract prime number theorem relating to algebraic function fields" Archiv der Math., 24 (1977), 271-279.
  27. " Generalised Euler constants" Proc. Edinburgh Math. Soc.,21 (1978), 25-32.
  28. " Recursive formulae for prime numbers", Archiv der Math., 33 (1979), 144-149.
  29. "Initial digits in number theory" , Fibonacci Quart., 19 (1981). 121-126.
  30. "Direct factors of polynomial rings over finite fields" J. Combinatorial Theory, Series A,40 (1985), 29-34.
  31. "Solomon s zeta function and enumeration of lattices over orders", Analysis, 5(1985), 29-42.
  32. "Solomon s zeta function over algebraic function fields" Manusripta Math., 53 (1985), 101- 106.
  33. "Normality of product expansions of power series over finite fields", Indian J. Pure and Appl. Math., 22 (1991), 627-632.
  34. "Ergodic properties of some inverse polynomial series expansions of Laurent series", Acta Math. Hungarica, 60 (1992), 291-296.
  35. "Enumerating non-equivalent matrices over principal ideal domains", Mathematica Slovaca , 44 (1994), 287-296.
  36. "Asymptotic isomer enumeration in chemistry", J. of Math. Chemistry 24 (1998), 61-69.

Refereed papers as joint author

  1. ( With A.M. Sinclair ) "Fields with few extensions", Proc. American Math. Soc., 29 (1971), 255-258.
  2. (With G.E. Burger) " Submodules, subalgebras and ideals in finite modules or nilpotent algebras over Dedekind domains," J. London Math. Soc. (2), 5 (1972), 681-690.
  3. (With J.N. Ridley) "Prime-independent arithmetical functions", Annali di Mat.Pura ed Appl., 101 (1974), 153-169.
  4. (With W. Schwarz) "Binomial expected values of arithmetical functions " J. f?r die reine und angew. Math ., 328 (1981), 84-98.
  5. (With W. Schwarz) "Binomial expected values of arithmetical functions ,II", Colloq. Math. Soc. J. Bolyai, 34 (1984), 863-904.
  6. (With A. Knopfmacher) "A new infinite product representation for real numbers", Monatshefte Math., 104 (1987), 29-44.
  7. (With A. Knopfmacher) "Two concrete constructions of the real numbers", Rocky Mtn. J. Math., 18 (1988), 813-824.
  8. (With A. Knopfmacher) "A new construction of the real numbers (via infinite products)", Nieuw Arch. Wisk., 5 (1987),19-31.
  9. (With A. Knopfmacher) "Infinite series representations for complex numbers", Rendiconti Circolo Mat. Palermo, 36 (1987), 434-456.
  10. (With A. Knopfmacher) " Representations for real numbers via k-th powers of integers", Fibonacci Quarterly, 27 (1989), 49-60.
  11. (With A. Knopfmacher) " A product representation for power series", Complex Variables - Theory & Appl., 10 (1988), 283-294.
  12. (With A. Knopfmacher) "Inverse polynomial expansions of Laurent series", Constructive Approximation, 4 (1988), 379-389.
  13. (With A. Knopfmacher) " A product expansion in p-adic and non- archimedean fields", Proc. American Math. Soc., 104 (1988), 1031-1035.
  14. (With A. Knopfmacher) "Infinite products for power series", J. Approximation Theory, 59 (1989), 276-281.
  15. (With A. Knopfmacher) "A binomial product representation for p-adic numbers", Archiv der Math., 52 (1989), 333-336.
  16. (With A. Knopfmacher) " Two constructions of the real numbers via alternating series", Int.J. Math. & Math. Sci., 12 (1989), 603-613.
  17. (With A. Knopfmacher) "Series expansions in p-adic and non- archimedean fields", J. Number Theory, 32 (1989), 297-306.
  18. (With A. Knopfmacher) " The exact length of the Euclidean algorithm in
  19. F-q-[x]", Mathematika, 35 (1988), 297-304.
  20. (With A. Knopfmacher) "P-adic and non-archimedean product representations", Resultate der Math., 15 (1989), 324-334.
  21. (With A. Knopfmacher) "Inverse polynomial expansions of Laurent series, II", J. Comp . Appl. Math., 28 (1989), 249-257.
  22. (With P.G. Slattery) "Ramanujan expansions over additive arithmetical semigroups", Bull. Soc. Math. Belgique, B41 (1989), 109-127.
  23. (With A. Knopfmacher & J.N. Ridley)Unique factorizations of formal power series" J. Math. Anal. Appl., 149 (1990), 402-411.
  24. (With S. Kalpazidou & A. Knopfmacher) "L?roth-type alternating series representations for real numbers", Acta Arith., 55 (1990), 311-322.
  25. (With A. Knopfmacher) "Counting polynomials with a given number of zeros in a finite field", Linear and Mult. Algebra, 26 (1990), 287-292.
  26. (With A. Knopfmacher) "The distribution of values of polynomials over a finite field", Linear Algebra & Appl.,134 (1990),145-151.
  27. (With A. Knopfmacher) "Normality of some p-adic product expansions", J. Australian Math. Soc., A49 (1990), 258-263.
  28. (With S. Kalpazidou & A. Knopfmacher) "Metric properties of alternating L?roth" series", Portugaliae Math., 48 (1991), 319-325.
  29. (With A. Knopfmacher) "The number of steps in the Euclidean algorithm over complex quadratic fields", BIT, 31 (1991), 286-292.
  30. (With K. -H. Indlekofer and R. Warlimont) " Arithmetical semigroups, I : Direct factors", Manuscr. Math., 71 (1991), 83-96.
  31. (With K. -H. Indlekofer and A. Knopfmacher) Alternating Balkema-Oppenheim expansions of real numbers, Bull. Soc. Math. Belgique, B44 (1992), 17-28.
  32. (With A. Knopfmacher and R. Warlimont) "Factorisatio numerorum in arithmetical semi groups" Acta Arithmetica, 61 (1992), 327-336.
  33. (With A. Knopfmacher) "Counting irreducible factors of polynomials over a finite field", Discrete Math., 112 (1993), 103-118.
  34. (With A. Knopfmacher) " Infinite series expansions for p-adic numbers", J. Number Theory, 41 (1992), 131-145.
  35. (With A. Knopfmacher) "Metric properties of algorithms inducing L?roth series expansions of Laurent series", Ast_risque, 209 (1992), 237-246.
  36. (With A. Knopfmacher) "Metric properties of some special p-adic series expansions", Acta Arith., 76 (1996), 11-19.
  37. (With ?. Porubsk) "Topologies related to arithmetical properties of integral domains", Expositiones Math., 15 (1997), 131-14
  38. "Arithmetical semigroups related to trees and polyhedra " (with Arnold Knopfmacher, S. Africa), J. of Combin. Theory , Ser. A. 86 (1999), 85-102.
  39. "Asymptotic isomer enumeration in chemistry,II" (with Richard Warlimont, Germany, ), J. of Math. Chemistry 26 (1999), 95-99.
  40. " A new approach to the Rogers-Ramanujan identities" (with George E. Andrews, U.S.A., and Arnold Knopfmacher, S. Africa,), J. Number Theory 80 (2000), 273-290.

Conference Papers

  1. "Some aspects of abstract analytic number theory," Invited Survey Lecture, Notices of South African Math. Soc., 12 (1980), 131-143.
  2. "Harmonic analysis of arithmetical functions", Proc. Symp. on Harmonic Analysis in Number Theory, RIMS, Kyoto University, June 29 - July 1, 1987; RIMS KUkyoroku, 631 (1987), 110-122.
  3. (With A. Knopfmacher) "Maximum length of the Euclidean algorithm and continued fractions in F(x)", Proc. 3rd Int. Congr. on Fibonacci Numbers, Pisa, 1988: "Applications of Fibonacci Numbers", Vol. 3, pp. 217-222 (Kluwer, Dordrecht, 1990).
  4. (With A. Knopfmacher), "An alternating product representation for real numbers", Proc. 3rd Int. Congr. on Fibonacci Numbers, Pisa, 1988: "Applications of Fibonacci Numbers", Vol.3, pp. 209-216 (Kluwer, Dordrecht,1990).
  5. (With A. Knopfmacher and R. Warlimont), "Ordered factorizations for integers and arithmetical semigroups", Advances in Number Theory (Proc. 3rd Conf. of Canadian Number Theory Assoc., 1991), pp. 151-165 (Clarendon Press, Oxford, 1993).
  6. (With A. Knopfmacher and R. Warlimont) " Lengths of factorizations for polynomials over a finite field", Contemp. Math.,168 (1994), 185-205.
  7. "Recent developments and applications of abstract analytic number theory", Invited Survey Lecture, Notices of South African Math. Soc., 28 (1996), 11-23.

Other Publications

"Some Aspects of the Theory of Prime Numbers", Inaugural Lecture, University of the Witwatersrand, Johannesburg (1979), 11pp.

Papers currently accepted or in preparation as of May 2001

"Averages and densities in the context of arithmetical semigroups related to trees and polyhedra" (with Arnold Knopfmacher, S. Africa), in preparation.

 

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