James P. Jones

Professor Emeritus

Department of Mathematics and Statistics


Contact information

Phone

Office: 403.210.6413

Web presence

Website

Location

Office : MS477

Research and teaching

Research areas

  • Mathematical logic
  • Recursion theory
  • Undecidability
  • Diophantine equations
  • Hilbert's Tenth Problem
  • Number theory

Publications

Journal article

  • Jones, James P.. "Representation of solutions of Pell equations using Lucas sequences". Acta Academiae Paedagogicae Agriensis. Nova Series. Sectio Matematicae 30. (2003): 75-86. Print.
  • Jones, James P. and Kiss, P. "Representation of integers as terms of a linear recurrence with maximal index". Acta Academiae Paedagogicae Agriensis. Nova Series. Sectio Matematicae 25. (1998): 21-37 (1999). Print.
  • Jones, James P. and Kiss, P. "Some new identities and congruences for Lucas sequences". Discussiones Mathematicae. Algebra 18.1 (1998): 39-47. Print.
  • Jones, James P., Levitz, Hilbert and Nichols, Warren D.. "On series of ordinals and combinatorics". Mathematical Logic Quarterly 43.1 (1997): 121-133. Print.
  • Jones, James P. and Fraenkel, A. S.. "Complexities of winning strategies in Diophantine games". Journal of Complexity 11.4 (1995): 435-455. Print.
  • Jones, James P.. "Diophantine representation of non-Fibonacci numbers". Kluwer Acad. Publ., (1993): 387-392. Print.
  • Jones, James P. and Kiss, P. "An asymptotic formula concerning Lehmer numbers". Publicationes Mathematicae Debrecen 42.3-4 (1993): 199-213. Print.
  • Jones, James P. and Kiss, P. "On points whose coordinates are terms of a linear recurrence". The Fibonacci Quarterly. The Official Journal of the Fibonacci Association 31.3 (1993): 239-245. Print.
  • Jones, James P. and Phong, B. M.. "Quadratic residues and related problems". Annales Univ. Sci. Budapest, Sect. Comp. 13.1 (1992): 149-155. Print.
  • Jones, James P. and Kiss, P.. "Some Diophantine approximation results concerning linear recurrences". Math. Slovaca 42.5 (1992): 583-591. Print.
  • Jones, James P. and Kiss, P.. "Exponential Diophantine representation of binomial coefficients, factorials and Lucas sequences". Discussiones Mathematicae 12. (1992): 53-65 (1993). Print.
  • Jones, James P. and Kiss, P. "Linear recursive sequences and power series". Publicationes Mathematicae Debrecen 41.3-4 (1992): 295-306. Print.
  • Tsangaris, P. G. and Jones, James P.. "An old theorem on the GCD and its application to primes". The Fibonacci Quarterly. Journal of the Fibonacci Assoc. 30.3 (1992): 194-198. Print.
  • Jones, James P.. "Computational complexity of computing winning strategies in polynomial games". Nanjing Daxue Xuebao. Shuxue Bannian Kan. Nanjing University. Journal. Mathematical Biquarterly 8.1 (1991): 1-5. Print.
  • Jones, James P. and Matiyasevich, Yuri V.. "Proof of recursive unsolvability of Hilbert's tenth problem". The American Mathematical Monthly 98.8 (1991): 689-709. Print.
  • Jones, James P. and Matiyasevich,Yuri V.. "Basis for the polynomial time computable functions". de Gruyter, (1990): 255-270. Print.
  • Jones, James P.. "Diophantine representation of Fibonacci numbers over natural numbers". Kluwer Acad. Publ., (1990): 197-201. Print.
  • Jones, James P.. "Basis for the Kalmar elementary functions". 265. Kluwer Acad. Publ., (1989): 435-444. Print.
  • Jones, James P., Levitz, H. and Wilkie, A. J.. "Classification of quantifier prefixes over exponential Diophantine equations". Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 32.5 (1986): 399-406. Print.
  • Jones, James P. and Matiyasevich, Yuri V.. "Register Machine proof of the Theorem on Exponential Diophantine representation of Enumerable sets". Journal of Symbolic Logic 49.3 (1984): 818-829. Print.
  • Jones, James P. and Matiyasevich,Yuri V.. "Direct Translation of Register Machines into Exponential Diophantine Equations". Fachbereich Mathematik Informatik Universitat Paderborn 1982.1 (1983): 117-130. Print.
  • Jones, James P. and Shepherdson, John C.. "Variants of Robinson's essentially undecidable theory R". Archiv fur Mathematische Logik und Grundlagenforschung 23.1-2 (1983): 61-64. Print.
  • Jones, James P. and Matiyasevich, Yuri V.. "Exponential Diophantine representation of recursively enumerable sets". Studies in Logic & Foundations of Math. North Holland, 107. (1982): 159-177. Print.
  • Dyson, Verena H., Jones, James P. and Shepherdson, John C.. "Some Diophantine forms of Godel's theorem". Archiv fur Mathematische Logik und Grundlagenforschung 22.1-2 (1982): 51-60. Print.
  • Jones, James P. and Matiyasevich,Yuri V.. "A new representation for the symmetric binomial coefficient and its applications". Les Annales des Sciences Mathematiques du Quebec 6.1 (1982): 81-97. Print.
  • Jones, James P.. "Some undecidable determined games". International Journal of Game Theory 11.2 (1982): 63-70. Print.
  • Jones, James P.. "Universal Diophantine equation". The Journal of Symbolic Logic 47.3 (1982): 549-571. Print.
  • Jones, James P.. "Classification of quantifier prefixes over Diophantine equations". Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 27.5 (1981): 403-410. Print.
  • Jones, James P.. "Undecidable Diophantine equations". American Mathematical Society. Bulletin. New Series 3.2 (1980): 859-862. Print.
  • Jones, James P.. "Diophantine representation of Mersenne and Fermat primes". Acta Arithmetica 35.3 (1979): 209-221. Print.
  • Jones, James P.. "Three universal representations of recursively enumerable sets". The Journal of Symbolic Logic 43.2 (1978): 335-351. Print.
  • Jones, James P., Sato, Daihachiro, Wada, Hideo and Wiens, Douglas. "Diophantine representation of the set of prime numbers". The American Mathematical Monthly 83.6 (1976): 449-464. Print.
  • Jones, James P.. "Diophantine representation of the Lucas numbers". The Fibonacci Quarterly. The Official Journal of the Fibonacci Association 14.2 (1976): 134. Print.
  • Jones, James P.. "Formula for the n-th prime number". Canadian Mathematical Bulletin. Bulletin Canadien de Math\'ematiques 18.3 (1975): 433-434. Print.
  • Jones, James P.. "Diophantine representation of the Fibonacci numbers". The Fibonacci Quarterly. The Official Journal of the Fibonacci Association 13. (1975): 84-88. Print.
  • Jones, James P.. "Recursive undecidability-an exposition". The American Mathematical Monthly 81. (1974): 724-738. Print.
  • Jones, James P. and Toporowski, S.. "Irrational numbers". The American Mathematical Monthly 80. (1973): 423-424. Print.
  • Jones, James P.. "Independent recursive axiomatizability in arithmetic". Proc. Amer. Math. Soc. 23. (1969): 107-113. Print.
  • Jones, James P.. "Effectively retractable theories and degrees of undecidability". The Journal of Symbolic Logic 34. (1969): 597-604. Print.