Edit Profile Loxton, John H. Compute Distance To: Compute Author ID: loxton.john-h Published as: Loxton, J. H.; Loxton, John; Loxton, John H. Documents Indexed: 52 Publications since 1972, including 2 Books Reviewing Activity: 194 Reviews all top 5 Co-Authors 16 single-authored 21 van der Poorten, Alfred J. 2 Sanders, John W. 2 Smith, Robert Arnold 1 Acreman, Dennis 1 Atan, Kamel Ariffin Mohd. 1 Barrucand, Pierre-A. 1 Bird, Gregory J. 1 Blanksby, P. E. 1 Erdős, Pál 1 Everest, Graham Robert 1 Glass, Jon P. 1 Hirschhorn, Michael D. 1 Khoo, David S. P. 1 Laohakosol, Vichian 1 Mignotte, Maurice 1 Said, Mohamad Rushdan Md 1 Seberry, Jennifer R. 1 Vaughan, Robert C. 1 Waldschmidt, Michel 1 Williams, Hugh Cowie 1 Yeung, Hang-Fai all top 5 Serials 8 Acta Arithmetica 7 Bulletin of the Australian Mathematical Society 6 Journal of the Australian Mathematical Society. Series A 5 Journal für die Reine und Angewandte Mathematik 3 Aequationes Mathematicae 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Journal of Number Theory 2 Mathematika 2 Comptes Rendus Mathématiques de l’Académie des Sciences 2 London Mathematical Society Lecture Note Series 1 Journal of the Australian Mathematical Society, Series B 1 Rocky Mountain Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Journal of the London Mathematical Society. Second Series 1 Journal and Proceedings of the Royal Society of New South Wales 1 Pacific Journal of Mathematics 1 Journal of Cryptology all top 5 Fields 49 Number theory (11-XX) 7 Difference and functional equations (39-XX) 4 General and overarching topics; collections (00-XX) 4 Computer science (68-XX) 3 Functions of a complex variable (30-XX) 3 Approximations and expansions (41-XX) 3 Information and communication theory, circuits (94-XX) 2 Field theory and polynomials (12-XX) 2 Numerical analysis (65-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Group theory and generalizations (20-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 47 Publications have been cited 279 times in 212 Documents Cited by ▼ Year ▼ Arithmetic properties of certain functions in several variables. III. Zbl 0339.10028Loxton, J. H.; van der Poorten, A. J. 26 1977 A class of hypertranscendental functions. Zbl 0384.10014Loxton, J. H.; van der Poorten, A. J. 18 1977 The estimation of complete exponential sums. Zbl 0575.10033Loxton, J. H.; Vaughan, R. C. 15 1985 Transcendence and algebraic independence by a method of Mahler. Zbl 0378.10020Loxton, J. H.; van der Poorten, A. J. 14 1977 Arithmetic properties of automata: regular sequences. Zbl 0656.10033Loxton, J. H.; van der Poorten, A. J. 12 1988 On the maximum modulus of cyclotomic integers. Zbl 0217.04203Loxton, J. H. 12 1972 Multiplicative relations in number fields. Zbl 0335.10023van der Poorten, A. J.; Loxton, J. H. 11 1977 Arithmetic properties of the solutions of a class of functional equations. Zbl 0468.10019Loxton, J. H.; van der Poorten, A. J. 10 1982 Algebraic independence properties of the Fredholm series. Zbl 0392.10034Loxton, J. H.; van der Poorten, A. J. 10 1978 Arithmetic properties of certain functions in several variables. II. Zbl 0339.10027Loxton, J. H.; van der Poorten, A. J. 10 1977 The graphs of exponential sums. Zbl 0517.10040Loxton, J. H. 8 1983 On Hua’s estimate for exponential sums. Zbl 0474.10030Loxton, John H.; Smith, Robert A. 8 1982 The kernel of a rule of approximate integration. Zbl 0418.41026Loxton, J. H.; Sanders, J. W. 8 1980 On the growth of recurrence sequences. Zbl 0348.10007Loxton, J. H.; van der Poorten, A. J. 8 1977 Arithmetic properties of certain functions in several variables. Zbl 0339.10026Loxton, J. H.; van der Poorten, A. J. 8 1977 Some problems involving powers of integers. Zbl 0549.10012Loxton, J. H. 7 1986 Special values of the dilogarithm function. Zbl 0485.10036Loxton, J. H. 7 1984 Multiplicative dependence in number fields. Zbl 0478.10019Loxton, J. H.; van der Poorten, A. J. 7 1983 A note on the characterization of CM-fields. Zbl 0413.12002Blanksby, P. E.; Loxton, J. H. 7 1978 On an inversion theorem of Möbius. Zbl 0445.10006Loxton, J. H.; Sanders, J. W. 6 1980 Some conjectures concerning Gauss sums. Zbl 0362.10033Loxton, J. H. 6 1978 Products related to Gauss sums. Zbl 0293.10019Loxton, J. H. 6 1974 Multi-dimensional generalizations of the Padé table. Zbl 0423.30033Loxton, J. H.; Van der Poorten, A. J. 5 1979 On two problems of R. M. Robinson about sums of roots of unity. Zbl 0263.12002Loxton, J. H. 5 1974 Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant. Zbl 0649.12003Barrucand, Pierre; Loxton, John; Williams, H. C. 4 1987 On algebraic functions satisfying a class of functional equations. Zbl 0339.12002Loxton, J. H.; van der Poorten, A. J. 4 1976 Estimates for complete multiple exponential sums. Zbl 0963.11044Loxton, J. H. 3 2000 A method of Mahler in transcendence theory and some of its applications. Zbl 0519.10022Loxton, J. H. 3 1984 Estimates for multiple exponential sums. Zbl 0493.10041Loxton, John H.; Smith, Robert A. 3 1982 Computing the effectively computable bound in Baker’s inequality for linear forms in logarithms, and: Multiplicative relations in number fields: Corrigenda and addenda. Zbl 0362.10019van der Poorten, A. J.; Loxton, J. H. 3 1977 Counting algebraic units with bounded height. Zbl 0786.11064Everest, G. R.; Loxton, J. H. 2 1993 A cubic RSA code equivalent to factorization. Zbl 0755.94008Loxton, J. H.; Khoo, David S. P.; Bird, Gregory J.; Seberry, Jennifer 2 1992 Number theory and cryptography. Papers presented at the 33rd annual meeting of the Australian Mathematical Society and at a workshop on number theory and cryptography in telecommunications held at Macquarie University in Sydney, Australia, from 29 June to 7 July 1989. Zbl 0695.00009Loxton, J. H. (ed.) 2 1990 Automata and transcendence. Zbl 0656.10032Loxton, J. H. 2 1988 An awful problem about integers in base four. Zbl 0636.10003Loxton, J. H.; van der Poorten, A. J. 2 1987 Diophantine analysis. Proceedings of the Number Theory Section of the 1985 Australian Mathematical Society Convention (University of New South Wales). Zbl 0583.00005Loxton, J. H. (ed.); van der Poorten, A. J. (ed.) 2 1986 Computing the effectively computable bound in Baker’s inequality for linear forms in logarithms. Zbl 0324.10012van der Poorten, A. J.; Loxton, J. H. 2 1976 Congruence properties of the binary partition function. Zbl 0314.10004Hirschhorn, M. D.; Loxton, J. H. 2 1975 A cubic analogue of the RSA cryptosystem. Zbl 1049.94014Said, Mohamad Rushdan Md.; Loxton, John 1 2003 Common summands in partitions. Zbl 0768.11040Loxton, J. H.; Yeung, Hang-Fai 1 1992 A lower bound for linear forms in the logarithms of algebraic numbers. Zbl 0623.10023Loxton, J. H.; Mignotte, M.; van der Poorten, A. J.; Waldschmidt, M. 1 1987 Newton polyhedra and solutions of congruences. Zbl 0601.12023Atan, Kamel A.; Loxton, J. H. 1 1986 Asymptotic analysis of Ramanujan pairs. Zbl 0588.10055Acreman, D.; Loxton, J. H. 1 1986 The distribution of exponential sums. Zbl 0574.10042Loxton, J. H. 1 1985 Some problems in partitio numerorum. Zbl 0403.10004Erdős, Paul; Loxton, J. H. 1 1979 On the determination of Gauss sums. Zbl 0373.10023Loxton, John H. 1 1977 On a cyclotomic diophantine equation. Zbl 0292.12007Loxton, J. H. 1 1974 A cubic analogue of the RSA cryptosystem. Zbl 1049.94014Said, Mohamad Rushdan Md.; Loxton, John 1 2003 Estimates for complete multiple exponential sums. Zbl 0963.11044Loxton, J. H. 3 2000 Counting algebraic units with bounded height. Zbl 0786.11064Everest, G. R.; Loxton, J. H. 2 1993 A cubic RSA code equivalent to factorization. Zbl 0755.94008Loxton, J. H.; Khoo, David S. P.; Bird, Gregory J.; Seberry, Jennifer 2 1992 Common summands in partitions. Zbl 0768.11040Loxton, J. H.; Yeung, Hang-Fai 1 1992 Number theory and cryptography. Papers presented at the 33rd annual meeting of the Australian Mathematical Society and at a workshop on number theory and cryptography in telecommunications held at Macquarie University in Sydney, Australia, from 29 June to 7 July 1989. Zbl 0695.00009Loxton, J. H. (ed.) 2 1990 Arithmetic properties of automata: regular sequences. Zbl 0656.10033Loxton, J. H.; van der Poorten, A. J. 12 1988 Automata and transcendence. Zbl 0656.10032Loxton, J. H. 2 1988 Some explicit upper bounds on the class number and regulator of a cubic field with negative discriminant. Zbl 0649.12003Barrucand, Pierre; Loxton, John; Williams, H. C. 4 1987 An awful problem about integers in base four. Zbl 0636.10003Loxton, J. H.; van der Poorten, A. J. 2 1987 A lower bound for linear forms in the logarithms of algebraic numbers. Zbl 0623.10023Loxton, J. H.; Mignotte, M.; van der Poorten, A. J.; Waldschmidt, M. 1 1987 Some problems involving powers of integers. Zbl 0549.10012Loxton, J. H. 7 1986 Diophantine analysis. Proceedings of the Number Theory Section of the 1985 Australian Mathematical Society Convention (University of New South Wales). Zbl 0583.00005Loxton, J. H. (ed.); van der Poorten, A. J. (ed.) 2 1986 Newton polyhedra and solutions of congruences. Zbl 0601.12023Atan, Kamel A.; Loxton, J. H. 1 1986 Asymptotic analysis of Ramanujan pairs. Zbl 0588.10055Acreman, D.; Loxton, J. H. 1 1986 The estimation of complete exponential sums. Zbl 0575.10033Loxton, J. H.; Vaughan, R. C. 15 1985 The distribution of exponential sums. Zbl 0574.10042Loxton, J. H. 1 1985 Special values of the dilogarithm function. Zbl 0485.10036Loxton, J. H. 7 1984 A method of Mahler in transcendence theory and some of its applications. Zbl 0519.10022Loxton, J. H. 3 1984 The graphs of exponential sums. Zbl 0517.10040Loxton, J. H. 8 1983 Multiplicative dependence in number fields. Zbl 0478.10019Loxton, J. H.; van der Poorten, A. J. 7 1983 Arithmetic properties of the solutions of a class of functional equations. Zbl 0468.10019Loxton, J. H.; van der Poorten, A. J. 10 1982 On Hua’s estimate for exponential sums. Zbl 0474.10030Loxton, John H.; Smith, Robert A. 8 1982 Estimates for multiple exponential sums. Zbl 0493.10041Loxton, John H.; Smith, Robert A. 3 1982 The kernel of a rule of approximate integration. Zbl 0418.41026Loxton, J. H.; Sanders, J. W. 8 1980 On an inversion theorem of Möbius. Zbl 0445.10006Loxton, J. H.; Sanders, J. W. 6 1980 Multi-dimensional generalizations of the Padé table. Zbl 0423.30033Loxton, J. H.; Van der Poorten, A. J. 5 1979 Some problems in partitio numerorum. Zbl 0403.10004Erdős, Paul; Loxton, J. H. 1 1979 Algebraic independence properties of the Fredholm series. Zbl 0392.10034Loxton, J. H.; van der Poorten, A. J. 10 1978 A note on the characterization of CM-fields. Zbl 0413.12002Blanksby, P. E.; Loxton, J. H. 7 1978 Some conjectures concerning Gauss sums. Zbl 0362.10033Loxton, J. H. 6 1978 Arithmetic properties of certain functions in several variables. III. Zbl 0339.10028Loxton, J. H.; van der Poorten, A. J. 26 1977 A class of hypertranscendental functions. Zbl 0384.10014Loxton, J. H.; van der Poorten, A. J. 18 1977 Transcendence and algebraic independence by a method of Mahler. Zbl 0378.10020Loxton, J. H.; van der Poorten, A. J. 14 1977 Multiplicative relations in number fields. Zbl 0335.10023van der Poorten, A. J.; Loxton, J. H. 11 1977 Arithmetic properties of certain functions in several variables. II. Zbl 0339.10027Loxton, J. H.; van der Poorten, A. J. 10 1977 On the growth of recurrence sequences. Zbl 0348.10007Loxton, J. H.; van der Poorten, A. J. 8 1977 Arithmetic properties of certain functions in several variables. Zbl 0339.10026Loxton, J. H.; van der Poorten, A. J. 8 1977 Computing the effectively computable bound in Baker’s inequality for linear forms in logarithms, and: Multiplicative relations in number fields: Corrigenda and addenda. Zbl 0362.10019van der Poorten, A. J.; Loxton, J. H. 3 1977 On the determination of Gauss sums. Zbl 0373.10023Loxton, John H. 1 1977 On algebraic functions satisfying a class of functional equations. Zbl 0339.12002Loxton, J. H.; van der Poorten, A. J. 4 1976 Computing the effectively computable bound in Baker’s inequality for linear forms in logarithms. Zbl 0324.10012van der Poorten, A. J.; Loxton, J. H. 2 1976 Congruence properties of the binary partition function. Zbl 0314.10004Hirschhorn, M. D.; Loxton, J. H. 2 1975 Products related to Gauss sums. Zbl 0293.10019Loxton, J. H. 6 1974 On two problems of R. M. Robinson about sums of roots of unity. Zbl 0263.12002Loxton, J. H. 5 1974 On a cyclotomic diophantine equation. Zbl 0292.12007Loxton, J. H. 1 1974 On the maximum modulus of cyclotomic integers. Zbl 0217.04203Loxton, J. H. 12 1972 all cited Publications top 5 cited Publications all top 5 Cited by 235 Authors 7 Shparlinski, Igor E. 7 Tanaka, Taka-aki 7 van der Poorten, Alfred J. 5 Adamczewski, Boris 5 Allouche, Jean-Paul Simon 5 Nishioka, Kumiko 5 Schmeisser, Gerhard 5 Tachiya, Yohei 4 Amou, Masaaki 4 Bugeaud, Yann 4 Lewin, Leonard 4 Louboutin, Stéphane R. 4 Loxton, John H. 4 Ostafe, Alina 4 Sha, Min 4 Väänänen, Keijo O. 3 Abouzahra, M. D. 3 Bundschuh, Peter 3 Evans, Ronald J. 3 Kurosawa, Takeshi 3 Kwon, DoYong 3 Masser, David William 3 Mauduit, Christian 3 Mendès France, Michel 3 Mignotte, Maurice 3 Nuttall, John 3 Rahman, Qazi Ibadur 3 Shiokawa, Iekata 3 Stan, Florin 3 Stewart, Cameron L. 3 Wen, Zhixiong 3 Zaharescu, Alexandru 2 Atan, Kamel Ariffin Mohd. 2 Becker, Paul-Georg 2 Berndt, Bruce Carl 2 Butzer, Paul Leo 2 Chamizo Lorente, Fernando 2 Cochrane, Todd 2 Coons, Michael 2 Ding, Ping 2 Dubickas, Artūras 2 Katsurada, Masanori 2 Laurent, Michel 2 Le, Maohua 2 Luca, Florian 2 Matthews, Charles Russell 2 Morrison, Scott 2 Nishioka, Keiji 2 Paris, Richard Bruce 2 Pellarin, Federico 2 Philippon, Patrice 2 Reshetukha, I. V. 2 Shallit, Jeffrey O. 2 Snyder, Noah 2 Tamura, Jun-ichi 2 Tanuma, Yusuke 2 Töpfer, Thomas 2 Waldschmidt, Michel 2 Wen, Zhi-Ying 2 Yu, Kunrui 2 Zaïmi, Toufik Mostepha 2 Zamboni, Luca Quardo 2 Zheng, Zhiyong 1 Acreman, Dennis 1 Adams, William W. 1 Ali, Zulkarnain Md 1 Anderson, Michael 1 Andrews, George Eyre 1 Arredondo, John Alexander 1 Aubry, Yves 1 Bailey, David Harold 1 Bank, Steven B. 1 Bardaro, Carlo 1 Beli, Constantin-Nicolae 1 Bell, Jason P. 1 Ben Arous, Gérard 1 Bennett, Michael A. 1 Bergweiler, Walter 1 Bernstein, Daniel Julius 1 Bertrand, Daniel 1 Beukers, Frits 1 Bézivin, Jean-Paul 1 Biggs, Norman L. 1 Biran, Paul 1 Borges, Joaquim 1 Borwein, Jonathan Michael 1 Borwein, Peter Benjamin 1 Bousquet-Mélou, Mireille 1 Brenner, Charles H. 1 Brinkhuis, Jan 1 Browning, Timothy Daniel 1 Buell, Duncan A. 1 Calegari, Frank 1 Cassaigne, Julien 1 Chalk, John H. H. 1 Chen, Evan 1 Chen, Gongliang 1 Chen, Jin 1 Chi, Dongpyo 1 Chirikov, Boris Valerianovich ...and 135 more Authors all top 5 Cited in 90 Serials 33 Journal of Number Theory 9 Journal de Théorie des Nombres de Bordeaux 8 Aequationes Mathematicae 7 Compositio Mathematica 6 Proceedings of the American Mathematical Society 6 Theoretical Computer Science 5 Mathematical Notes 5 Transactions of the American Mathematical Society 5 Indagationes Mathematicae. New Series 4 Inventiones Mathematicae 4 Journal of Combinatorial Theory. Series A 4 International Journal of Number Theory 3 Journal of Mathematical Analysis and Applications 3 Annales de l’Institut Fourier 3 Archiv der Mathematik 3 Journal of Approximation Theory 3 Monatshefte für Mathematik 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Acta Mathematica Academiae Scientiarum Hungaricae 2 Bulletin of the Australian Mathematical Society 2 Acta Arithmetica 2 Glasgow Mathematical Journal 2 Journal of Computational and Applied Mathematics 2 Journal of Soviet Mathematics 2 Manuscripta Mathematica 2 Mathematika 2 Numerische Mathematik 2 Proceedings of the London Mathematical Society. Third Series 2 Results in Mathematics 2 Tohoku Mathematical Journal. Second Series 2 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques 2 Acta Mathematica Hungarica 2 Journal of the American Mathematical Society 2 Designs, Codes and Cryptography 2 Linear Algebra and its Applications 2 Bulletin of the American Mathematical Society. New Series 2 Journal of Mathematical Sciences (New York) 2 The Ramanujan Journal 2 Integers 1 Communications in Mathematical Physics 1 Discrete Mathematics 1 International Journal of Mathematical Education in Science and Technology 1 Israel Journal of Mathematics 1 Problems of Information Transmission 1 Rocky Mountain Journal of Mathematics 1 Ukrainian Mathematical Journal 1 Mathematics of Computation 1 Chaos, Solitons and Fractals 1 The Mathematical Intelligencer 1 Acta Mathematica 1 Advances in Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Calcolo 1 Commentationes Mathematicae Universitatis Carolinae 1 Duke Mathematical Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Journal für die Reine und Angewandte Mathematik 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Mathematische Zeitschrift 1 Michigan Mathematical Journal 1 Nagoya Mathematical Journal 1 Proceedings of the Japan Academy. Series A 1 Quaestiones Mathematicae 1 Tokyo Journal of Mathematics 1 Topology and its Applications 1 European Journal of Combinatorics 1 Ergodic Theory and Dynamical Systems 1 Combinatorica 1 Physica D 1 Applied Numerical Mathematics 1 Journal of Symbolic Computation 1 Constructive Approximation 1 Revista Matemática Iberoamericana 1 Journal of Cryptology 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 1 Acta Mathematica Sinica. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Experimental Mathematics 1 Applied and Computational Harmonic Analysis 1 Finite Fields and their Applications 1 The New York Journal of Mathematics 1 Documenta Mathematica 1 Acta Mathematica Sinica. English Series 1 Qualitative Theory of Dynamical Systems 1 Journal of the Australian Mathematical Society 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Journal of Modern Dynamics all top 5 Cited in 34 Fields 181 Number theory (11-XX) 19 Computer science (68-XX) 13 Dynamical systems and ergodic theory (37-XX) 12 Approximations and expansions (41-XX) 11 Difference and functional equations (39-XX) 10 Special functions (33-XX) 9 Algebraic geometry (14-XX) 9 Functions of a complex variable (30-XX) 9 Numerical analysis (65-XX) 8 Combinatorics (05-XX) 7 Real functions (26-XX) 6 Functional analysis (46-XX) 6 Information and communication theory, circuits (94-XX) 4 Field theory and polynomials (12-XX) 3 Commutative algebra (13-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Probability theory and stochastic processes (60-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Measure and integration (28-XX) 2 Sequences, series, summability (40-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Geometry (51-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) Citations by Year