List of Publications of R. Tijdeman. 2. On the distribution of the values of certain functions. Thesis, Univ. of Amsterdam, 1969.

Transcription

1 List of Publications of R. Tijdeman 1. On a conjecture of Turán and Erdős, Indag. Math. 28 (1966), = Proc. KNAW Ser. A 69 (1966), On the distribution of the values of certain functions. Thesis, Univ. of Amsterdam, On an inequality of P. Turán, Acta Math. Acad. Sci. Hungar. 21 (1970), On the number of zeros of general exponential polynomials, Indag. Math. 33 (1971), 1-7 = Proc. KNAW Ser. A. 74 (1971), On the algebraic independence of certain numbers, Indag. Math. 33 (1971), = Proc. KNAW Ser. A 74 (1971), On a telephone problem, Nieuw Arch. Wiskunde (3) 19 (1971), Note on Mahler s Problem, K. Norske Vidensk. Selsk. Skr. 1972, No. 16, 4p. 8. Old and new in number theory, Nieuw Arch. Wiskunde (3) 20 (1972), On the maximal distance of numbers with a large prime factor, J. London Math. Soc. (2) 5 (1972), An auxiliary result in the theory of transcendental numbers, J. Number Theory 5 (1973), (With P.L. Cijsouw), Distinct prime factors of consecutive integers, Diophantine Approximation and its Applications, ed. by C.F. Osgood, Ac. Press, New York, 1973, (With A.A. Balkema), Some estimates in the theory of exponential sums, Acta. Math. Acad. Sci. Hungar. 24 (1973), (With P.L. Cijsouw), On the transcendence of certain power series of algebraic numbers, Acta. Arith. 23 (1973), On the distribution problem in finite and countable sets, J. Combin. Th. Ser. A 15 (1973), On integers with many small prime factors, Compositio Math. 26 (1973), On the maximal distance between integers composed of small primes, Compositio Math. 28 (1974), (With H. Leenman), Bounds for the maximum modulus of the first k power sums, Indag. Math. 36 (1974), = Proc. KNAW Ser. A 77 (1974),

2 18. (With H.G. Meijer), On additive functions, Compositio Math. 29 (1974), (With H.G. Meijer), On integers generated by a finite number of fixed primes, Compositio Math. 29 (1974), (With K. Ramachandra and T.N. Shorey), On Grimm s problem relating to factorisation of a block of consecutive integers, J. reine angew. Math. 273 (1975), (With P.L. Cijsouw), An auxiliary result in the theory of transcendental numbers, Duke Math. J. 42 (1975), Some applications of Baker s sharpened bounds to diophantine equations, Séminaire Delange-Pisot-Poitou (Théorie des nombres), 16e année 1974/75, no (With A.J. van der Poorten), On common zeros of exponential polynomials, L Enseignement Math. 21 (1975), (With M. Voorhoeve and A.J. van der Poorten), On the number of zeros of certain functions, Indag. Math. 37 (1975), = Proc. KNAW Ser. A 78 (1975), On the equation of Catalan, Acta Arith. 29 (1976), On the Gel fond-baker method and its applications, Proc. Sympos. Pure Math. Amer. Math. Soc. 28 (1976), Applications of the Gel fond-baker method to rational number theory, Colloquia Math. Soc. János Bolyai, 13. Topics in number theory, Debrecen, 1974, pp (With T.N. Shorey), On the greatest prime factors of polynomials at integer points, Compositio Math. 33 (1976), (With A. Schinzel), On the equation y m = P(x), Acta Arith. 31 (1976), (With K. Ramachandra and T.N. Shorey), On Grimm s problem relating to factorisation of a block of consecutive integers II, J. reine angew. Math. 288 (1976), (With T.N. Shorey), New applications of diophantine approximations to diophantine equations, Math. Scand. 39 (1976), (With T.N. Shorey, A.J. van der Poorten and A. Schinzel), Applications of the Gel fond- Baker method to diophantine equations, Transcendence Theory, Advances and Applications, Proc. Conf. Cambridge 1976, ed. by A. Baker and D.W. Masser, Ac. Press, London, 1977, pp Distance sets of sequences of integers, Proc. Bicentennial Congress Wiskundig Genootschap, Math. Centre Tract 101, Part II, 1978, pp

3 34. (With M. Voorhoeve and K. Győry), On the Diophantine equation 1 k +2 k +...+x k +R(x) = y z, Acta Math. 143 (1979), 1-8. Corr. 159 (1987), (With C.L. Stewart), On infinite-difference sets, Can. J. Math. 31 (1979), Exponential diophantine equations, Proc. Intern. Congress Math. Helskini Acad. Sci. Fenn., Helsinki 1980, pp The Chairman Assignment Problem, Discrete Math. 32 (1980), (With G. Wagner), A sequence has almost nowhere small discrepancy, Monatsh. Math. 90 (1980), (With K. Győry and M. Voorhoeve), On the equation 1 k + 2 k x k = y z, Acta Arith. 37 (1980), (With M. Voorhoeve), Bounded discrepancy sets, Compositio Math. 42 (1980), Solvability of diophantine equations, Nieuw Arch. Wiskunde (3) 29 (1981), On the discrepancy of a sequence in [0, 1), Sém. de Th. des Nombres, Paris , ed. by M.J. Bertin, Birkhäuser, 1981, pp (With A.E. Brouwer), On the edge-colouring problem for unions of complete uniform hypergraphs, Discrete Math. 34 (1981), Multiplicities of binary recurrences, Sém Théorie Nombr , Univ. Bordeaux, Exp. no. 29 (1982), 11 pp. 45. A progress report on discrepancy, Journées Arithmétiques Metz 1981, Astérisque 94, Soc. Math. France, 1982, pp (With R.J. Stroeker and appendix by P.L. Cijsouw, A. Korlaar and R. Tijdeman), Diophantine equations, Computational methods in number theory, ed. by H.W. Lenstra Jr. and R. Tijdeman, MC. Tracts , Mathematical Centre, Amsterdam, 1983, pp (With T. Salát), Asymptotic densities of sets of positive integers, Math. Slovaca 33 (1983), (With C.L. Stewart), On density-difference sets of sets of integers, Studies in Pure Mathematics dedidated to the memory of Paul Turán, Akad. Kiadó, Budapest, 1983, pp (With F. Beukers), On the multiplicaties of binary complex recurrences, Compositio Math. 51 (1984),

4 50. (With M. Mignotte and T.N. Shorey), The distance between terms of an algebraic recurrence sequence, J. reine angew. Math. 349 (1984), (With T. Salát), On density measure sets of positive integers, Coll. Math. Soc. János Bólyai, 34 Topics in Classical Number Theory, Budapest (Hungary), 1981, pp (1984). 52. On the Fermat-Catalan equation, Jber. d. Dt.-Verein 87 (1985), (With G. Brown and W. Moran), Riesz products are basic measures, J. London Math. Soc. (2) 30 (1984), (With B. Brindza and K. Győry), The Fermat equation with polynomial values as base variables, Invent. Math. 80 (1985), (With B. Brindza and K. Győry), On the Catalan equation over algebraic number fields, J. reine angew. Math. 367 (1986), (With K. Győry and C.L. Stewart), On prime factors of sums of integers I, Compositio Math. 59 (1986), (With C.L. Stewart), On prime factors of sums of integers II, In: Diophantine Analysis, Proc. Number Theory Section Austr. Math. Soc. Convention, ed. by J.H. Loxton and A.J. van der Poorten, London Math. Soc. Lect. Note Series 109, Cambridge Univ. Press, 1986, pp Approximations of real matrices by integral matrices, J. Number Theory 24 (1986), (With T.N. Shorey), Exponential Diophantine Equations, Cambridge Tracts in Mathematics 87, Cambridge University Press, Cambridge, 1986, 240 pp. 60. (With C.L. Stewart), On the Oesterlé-Masser conjecture, Monatsh. Math. 102 (1986), (With J.-H. Evertse, K. Győry and T.N. Shorey), Equal values of binary forms at integral points, Acta. Arith. 48 (1987), A note on the Fermat equation, Colloq. Math. 54 (1987), (With K. Győry and C.L. Stewart), On prime factors of sums of integers III, Acta Arith. 49 (1988), (With P. Erdős and C.L. Stewart), Some diophantine equations with many solutions, Compositio Math. 66 (1988), (With L. Wang), Sums of products of powers of given prime numbers, Pacific J. Math. 132 (1988), Corr. 135 (1988),

5 66. (With J.-H. Evertse, K. Győry and C.L. Stewart), On S-unit equations in two unknowns, Invent. Math. 92 (1988), (With Lianxiang Wang), Simultaneous weighted sums of elements of finitely generated multiplicative groups, Proc. KNAW Ser A 91 = Indag. Math. 50 (1988), (With J.-H. Evertse, K. Győry and C.L. Stewart), S-unit equations and their applications, New Advances in Transcendence Theory, ed. by A. Baker, Cambridge University Press, Cambridge etc., 1988, pp Diophantine equations and diophantine appromimations, Number Theory and Applications, ed. by R. A. Mollin, NATO ASI Ser. C, Vol 265, Kluwer, Dordrecht etc., 1989, pp On the product of the terms of a finite arithmetic progression, Proc. Conf. Diophantine Approximations and Transcendence Theory, ed. by Y.-N. Nakai, RIMS Kokyuroku 708, Kyoto University, Kyoto, Japan (1990), pp (With T.N. Shorey), Perfect powers in arithmetical progressions, J. Madras Univ. B 51 (1988), (published in 1990). 72. The number of solutions of diophantine equations, Colloq. Mathem. Soc. János Bolyai, 51, Number Theory, Budapest, 1987, pp (1990). 73. (With R.J. Kooman), Convergence properties of linear recurrence sequences. Nieuw Arch. Wiskunde (4) 8 (1990), (With T.N. Shorey), Perfect powers in products of terms in an arithmetical progression, Compositio Math. 75 (1990), (With T.N. Shorey), On the number of prime factors of an arithmetical progression, Sichuan Daxue Xuebao (J. Sichuan Univ. Natur. Sc. Ed.) 26 (1989), (With T.N. Shorey), On the greatest prime factor of an arithmetical progression (II), Acta Arith. 53 (1990), (With T.N. Shorey), On the greatest prime factor of an arithmetical progression, In: A Tribute to Paul Erdős, ed. by A. Baker, B. Bollabás and A. Hajnal, Cambridge University Press, 1990, pp (With R.W. Goldbach), Pairings of 2n points on a circle, Utilitas Math. 38 (1990), (With I.Z. Ruzsa), On the difference of integer-valued additive functions, Publ. Math. Debrecen 39 (1991), (With T.N. Shorey), Perfect powers in arithmetical progression (II), Compositio Math. 82 5

6 (1992), (With T.N. Shorey), Perfect powers in products of terms in an arithmetical progression (II), Compositio Math. 82 (1992), (With Mo Deze), Exponential diophantine equations with four terms, Indag. Math. (2) 3 (1992), (With T.N. Shorey), On the greatest prime factor of an arithmetical progression (III), Approximations Diophantiennes et Nombres Transcendants, Luminy 1990, ed. by P. Philippon, Walter de Gruyter, Berlin, 1992, pp (With T.N. Shorey), On the number of prime factors of a finite arithmetical progression, Acta Arith. 61 (1992), (With T.N. Shorey), Perfect powers in products of terms in an arithmetical progression III, Acta Arith. 61 (1992), Diophantine approximation and its applications, In: Diophantine Approximation and Abelian Varieties, ed. by B. Edixhoven and J.-H. Evertse, Lect. Notes Math (1993) Springer-Verlag, Berlin etc., 1993, pp Roth s Theorem, ibid, pp (With N. Saradha and T.N. Shorey), On arithmetic progressions with equal products, Acta Arith. 68 (1994), (With N. Saradha and T.N. Shorey), On arithmetic progressions of equal lengths with equal products, Math. Proc. Camb. Phil. Soc. 117 (1995), Decomposition of the integers as a direct sum of two subsets, Number Theory, ed. by S. David, Number Theory Seminar Paris , Cambridge University Press, 1995, pp (With N. Saradha and T.N. Shorey), On the equation x(x+1)...(x+k 1) = y(y+d)...(y+ (mk 1)d), m = 1, 2, Acta Arith. 71 (1995), (With N. Saradha and T.N. Shorey), On values of a polynomial at arithmetic progressions with equal products, Acta Arith. 72 (1995), On complementary triples of Sturmian bisequences, Indag. Math. N.S. 7(1996), (With J.-H. Evertse), Singular differences of powers of 2 2 matrices, Compositio Math. 104 (1996), (With T.N. Shorey), Some methods of Erdős applied to finite arithmetic progressions, The Mathematics of Paul Erdős, ed. by E.L. Graham and J. Nesetril, Algorithms and 6

7 Combinatorics 13, Springer-Verlag Berlin etc., 1996, pp (With G.N. ten Have), Diophantine approximations of matrices, Rocky Mountain J. Math. 26 (1996), (With C.L. Stewart), On the greatest prime factor of (ab + 1)(ac + 1)(bc + 1), Acta Arith. 97 (1997), (with T.N. Shorey) Irrationality criteria for numbers of Mahler s type, in: Analytic Number Theory, ed. by Y. Motohashi, London Math. Soc. LNS 247, Cambridge University Press, 1997, pp Intertwinings of periodic sequences, Indag. Math. 9 (1998), Exponential diophantine equations, in: Number Theory, ed. by K. Győry, A. Pethő, and V. Sos, Walter de Gruyter, Berlin etc., 1998, pp On the minimal complexity of infinite words, Indag. Math. N.S. 10 (1999), (with F. Beukers and T.N. Shorey) Irreducibility of polynomials and arithmetic progressions with equal products of terms, Number Theory in Progress, Proc. Conf. in honor of A. Schinzel, Zakopane, Poland, Vol. 1, Diophantine Problems and Polynomials, Walter de Gruyter, Berlin etc. 1999, pp (with G. Barat and R.F. Tichy) Digital blocks in linear numeration systems, in: Number Theory in Progress, Proc. Conf. in honor of A. Schinzel, Zakopane, Poland, Vol.2, Elementary and Analytic Number Theory, Walter de Gruyter, Berlin etc., 1999, pp (with J.W. Sander) Low complexity functions and convex sets in Z k, Math. Z. 233 (2000), Exact covers of balanced sequences and Fraenkel s conjecture, in: Algebraic Number Theory and Diophantine Analysis, Proc. Intern. Conf. Graz Austria, ed. by F. Halter-Koch and R.F. Tichy, Walter de Gruyter, Berlin etc., 2000, pp (with A. Heinis) Characterisation of asymptotically Sturmian sequences, Publ. Math. Debrecen 56 (2000), Fraenkel s conjecture for six sequences, Discrete Math. 222 (2000), (with J.W. Sander) The complexity of functions on lattices, Theoretical Computer Science 246 (2000), (with L. Hajdu) Algebraic aspects of discrete tomography, J. reine angew. Math. 534 (2001),

8 110 (with S.D. Adhikari, N. Saradha, T.N. Shorey) Transcendental infinite sums, Indag. Math. N.S. 12 (2001), (with L. Hajdu) An algorithm for discrete tomography, Linear Algebra Appl. 339 (2001), (with J. Sander) The rectangular complexity of functions on two-dimensional lattices, Theor. Computer Sci. 270 (2002), (with V. Berthé) Balance properties of multi-dimensional words, Theor. Computer Sci. 273 (2002) (with N. Saradha and T.N. Shorey) Some extensions and refinements of a theorem of Sylvester, Acta Arith. 102 (2002), Some applications of diophantine approximation, Number Theory for the Millennium III, ed. by M.A. Bennett et al., A K Peters, Natick USA, 2002, pp Also published in: Surveys in Number Theory, same data, (with Pingzhi Yuan) On the rationality of Cantor and Ahmes series, Indag. Math. N.S. 13 (2002), (with L. Hajdu) Algebraic aspects of emission tomography with absorption, Theor. Computer Sci. 290 (2003), (with J.H. Evertse, P. Moree, C.L. Stewart) Multivariate Diophantine equations with many solutions, Acta Arith. 107 (2003), (with L. Hajdu) Polynomials dividing infinitely many quadrinomials or quintinomials, Acta Arith. 107 (2003), (with R.J. Simpson) Multi-dimensional versions of a theorem of Fine and Wilf and a formula of Sylvester, Proc. Amer. Math. Soc. 131 (2003), (with N. Saradha) On the transcendence of infinite sums of values of rational functions, J. London Math. Soc. (3) 67 (2003), (with L. Zamboni) Fine and Wilf words for any periods, Indag. Math. N.S. 14 (2003), (with V. Berthé) Lattices and multi-dimensional words, Theor. Computer Sci. 319 (2004), (with J. Hančl) On the irrationality of Cantor series, J. reine angew. Math. 571 (2004),

9 125 (with J. Hančl) On the irrationality of Cantor and Ahmes series, Publ. Math. Debrecen 65 (2004), (with J. Hančl) On the irrationality of factorial series, Acta Arith. 118 (2005), (with S. Rosema) The tribonacci substitution, Integers, Electronic J. Combinatorial Number Th. 5 (3) (2005) A 13, 21 pp. 128 Rauzy substitutions and multi-dimensional Sturmian words, Theor. Computer Sci. 346 (2005), Periodicity and almost-periodicity, More Sets, Graphs and Numbers, ed. by E. Györi, Gy.O.H. Katona, and L. Lovász, Springer, Berlin etc., 2006, pp (with C. Fuchs) Substitutions, abstract number systems and the space filling property, Annal. Inst. Fourier Grenoble 56 (2006), (with A. Alpers) The two-dimensional Prouhet-Tarry-Escott problem, J. Number Th. 123 (2007), (with T.N. Shorey) Prime factors of arithmetic progressions and binomial coefficients, Diophantine Geometry, ed. by U. Zannier, CRM Series No. 4, Edizione Della Normale, 2007, pp (with L. Hajdu) Algebraic discrete tomography, Ch. 4 of Advances in Discrete Tomography and its Applications, ed. by G.T. Herman and A. Kuba, Birkhäuser, Boston etc., 2007, pp (with N. Hirata-Kohno, S. Laishram, T.N. Shorey) An extension of a theorem of Euler, Acta Arith. 129 (2007), (with A. Hajdu, L. Hajdu) General neighborhood sequences in Z n, Discr. Appl. Math. 155 (2007), (with N. Saradha) Arithmetic progression with common difference divisible by small primes, Acta Arith. 131 (2008), Highlights in the research work of T.N. Shorey, Diophantine Equations, ed. by N. Saradha, TIFR, Narosa Publ., New Delhi, India, 2008, pp On irrationality and transcendency of infinite sums of rational numbers, Diophantine Equations, ed. by N. Saradha, TIFR, Narosa Publ., New Delhi, India, 2008, pp (with J. Hančl) On the irrationality of polynomial Cantor series, Acta Arith. 133 (2008),

10 140 (with L. Hajdu) A criterion for polynomials to divide infinitely many k-nomials, Diophantine Approximation, Developments in Mathematics, Vol. 16, Springer-Verlag, Wien, pp (with L. Hajdu, Sz. Tengely) Cubes in products of terms in arithmetic progression, Publ. Math. Debrecen, 74 (2009), (with L. Zamboni) Fine and Wilf words for any periods II, Theor. Comput. Sci. 410 (2009), (with L. Zamboni) Characterizations of words with many periods, Integers 9 (2009), (with J. Hančl) On the irrationality of factorial series II, J. Number Th. 130 (2010),