Paul Thomas Young


Education

  • Doctor of Philosophy, Mathematics , Oklahoma State University , 1988.
  • Thesis:  "Radii of p-adic convergence of generic solutions of homogeneous linear differential equations"

  • Visiting Doctoral Student, Mathematics , Princeton University , 1987.

  • Master of Science, Mathematics , Oklahoma State University , 1985.

  • Bachelor of Science Summa Cum Laude, Mathematics, Lawrence Technological University , 1983.

  • Experience

  • Professor of Mathematics, College of Charleston

  • Charleston, South Carolina, 2002-present. Associate Professor, 1995-2002; Assistant Professor, 1991-95.
     
  • Assistant Professor, Tennessee Technological University

  • Cookeville, Tennessee, 1990-91.
     
  • Visiting Assistant Professor, University of Arkansas

  • Fayetteville, Arkansas, 1989-90.
     
  • Teaching Associate, Oklahoma State University

  • Stillwater, Oklahoma, 1985-89. Teaching Assistant, 1983-85.
     
  • Actuarial Student, Maccabees Mutual Life

  • Southfield, Michigan, 1982-84. Developed software.


    Professional

  • Member, American Mathematical Society, Mathematical Association of America, Fibonacci Association.

  • Programs Director, Pi Mu Epsilon, Oklahoma Beta Section, 1985-87.

  • Reviewer, Mathematical Reviews, 1993-present.

  • Referee, Journal of Number Theory; Journal für die Reine und Angewandte Mathematik; Acta Arithmetica; Duke Mathematical Journal; Finite Fields and Applications; Proceedings of the London Mathematical Society; Discrete Mathematics; The Fibonacci Quarterly; INTEGERS; Applied Mathematics Letters; American Mathematical Monthly; Logic and Analysis; European Journal of Pure and Applied Mathematics; Journal of Computational and Applied Mathematics; Journal of the Korean Mathematical Society; Annales des Sciences Mathématiques du Québec; Applied Mathematics & Information Sciences; Publicationes Mathematicae Debrecen; Computers and Mathematics with Applications; Mathematical Proceedings of the Royal Irish Academy; The Fibonacci Association International Conference Proceedings; Far East Journal of Mathematical Sciences; Discrete Dynamics in Nature and Society; Far East Journal of Applied Mathematics; Soochow Journal of Mathematics.

  • Organizer, Palmetto Number Theory Seminar Meeting 3, 2007; Meeting 7, 2008.

  • Organizer, Seventeenth Annual South Eastern Regional Meeting On Numbers, 2004.

  • Organizer, Eighth Annual South Eastern Regional Meeting On Numbers, 1995.

  • Presentations

  • "Algebraic and Topological Properties of p-adic Fields", MAA, 1985.

  • "The Diophantine Equation x^2+y^2=z^k", MAA, 1986.

  • "Application of Euler's Method of Continued Fractions to the p-adic Riccati Equation", MAA, 1988.

  • "Linear Differential Equations: The Complex and p -adic Theories", MAA, 1989.

  • "On Conics and Cubics and p-adic Methods", Seminar, 1989.

  • "On Apéry Numbers I, II, III, IV", OSU Number Theory Seminar, 1989-90.

  • "On Apéry Numbers and p-adic Hypergeometric Functions", AMS, 1991.

  • "p-adic Unit-Root Formulae from Formal Group Laws", SERMON, 1992.

  • "On p-adic hypergeometric functions and formal group laws", AMS Special Session, 1992.

  • "Quadratic Reciprocity via Lucas Sequences", SERMON, 1993.

  • "On the Gross-Koblitz Formula", Japan-U.S. Mathematics Institute Conference on Zeta Functions in Number Theory, 1993; Second International Conference on Finite Fields, 1993.

  • "Formal Group Laws in Number Theory", Five Colleges Number Theory Seminar, U. Mass., Amherst, 1993.

  • "Congruences for Generalized Dickson Polynomials", SERMON, 1994.

  • "On Generalized Dickson Polynomials", IMA Conference on Applications of Finite Fields, 1994.

  • "On a Class of Congruences for Lucas Sequences", Sixth International Conference on Fibonacci Numbers and their Applications, 1994.

  • "Some Congruences and Identities for Generalizations of Rédei Functions", Third International Conference on Finite Fields, 1995.

  • "On Dickson Polynomials, Rédei Functions, and Formal Group Laws", AMS Special Session, 1995.

  • "Introduction to Formal Group Laws", MAA Short Course, 1998.

  • "Kummer Congruences for Higher-Order Bernoulli Numbers", SERMON, 1998.

  • "Generalized Kummer Congruences", SERMON, 1999.

  • "A Compositeness Test Based on Modified Dickson Polynomials", SERMON, 2000.

  • "Primality Testing with Modified Dickson Polynomials", Ninth International Conference on Fibonacci Numbers and their Applications, 2000.

  • "Congruences for Degenerate Number Sequences", AMS Special Session, 2001.    

  • "Gauss Sums and Multinomial Coefficients", SERMON, 2003.

  • "Sums of Powers and Kummer's Congruences", Colloquium, UNC - Greensboro, 2004.

  • "On Lucas-Bernoulli Numbers", SERMON, 2006.  

  • "Bernoulli Numbers and Sums of Powers", Clemson ADM Seminar, 2006.  

  • "Bernoulli Polynomials and Sums of Powers", Séminaire de Theorie des Nombres, Institut de Mathématiques de Bordeaux, 2007.  

  • "A 2-adic Formula for Bernoulli Numbers of the Second Kind", Palmetto Number Theory Seminar V, 2008.  

  • "On the 2-adic Digits of Bernoulli Numbers of the Second Kind", MAA Special Session, 2008.  

  • "A p-adic Formula for the Nörlund Numbers", Thirteenth International Conference on Fibonacci Numbers and their Applications, 2008.  

  • "Questions Arising From the Factorization of Degenerate Bernoulli Numbers", Palmetto Number Theory Seminar VII, 2008. 

  • "Bernoulli Numbers and Generalized Factorial Sums", INTEGERS Conference, 2009.

  • "Generalizations of Bernoulli Numbers", invited colloquium, Instituto de Matemáticas Unidad Morelia, 2009

  • "Generalizations of Bernoulli Numbers and Factorial Sums", Fourteenth International Conference on Fibonacci Numbers and their Applications, 2010.  

  • "On the Binary Expansion of the Odd Catalan Numbers and p-adic Congruences for pq-Catalan Numbers", Fourteenth International Conference on Fibonacci Numbers and their Applications, 2010.   

  • "On p-adic Multiple Zeta and Log Gamma Functions", Palmetto Number Theory Seminar XIII, 2010.

  • "Arithmetic and Combinatorics of Bernoulli Numbers", invited colloquium, University of the Witwatersrand, Johannesburg, South Africa, 2011. 

    "The Combinatorics and Arithmetic of Bernoulli Numbers", invited seminar, University of North Carolina, Greensboro, 2011. 

    "Generalizations of Bernoulli Numbers in Number Theory and Combinatorics", invited seminar, Ostravská Univerzita, Ostrava, Czech Republic, 2012. 

    "On the Roots of the Degenerate Bernoulli numbers", Fifteenth International Conference on Fibonacci Numbers and their Applications, 2012.

    "Explicit Computation of Gross-Stark Units Over Real Quadratic Fields", West Coast Number Theory Conference, 2012. 

    "Rational Series for Multiple Zeta and Log Gamma Functions", SERMON, 2013. 


    Publications

    [1]  "Radii of convergence and index for p-adic differential operators", Transactions of the American Mathematical Society 333.2 (1992), 769-785.  [MR 92m:12015]  [Zbl 762.12005]

    [2] "Apéry numbers, Jacobi sums, and special values of generalized p-adic hypergeometric functions", Journal of Number Theory 41.2 (1992), 231-255.  [MR 93j:11079]  [Zbl 759.11042]

    [3] "p-adic congruences for generalized Fibonacci sequences", The Fibonacci Quarterly 32.1 (1994), 2-10.  [MR 95a:11014]  [Zbl 803.11016]

    [4] "On the Gross-Koblitz formula", Contemporary Mathematics 168 (1994), 379-386.  [MR 95m:11087]  [Zbl 874.11056]

    [5] "Quadratic reciprocity via Lucas sequences", The Fibonacci Quarterly 33.1 (1995), 78-81.  [MR 95m:11011]  [Zbl 826.11004]

    [6] "On Jacobi sums, multinomial coefficients, and p-adic hypergeometric functions", Journal of Number Theory 52.1 (1995), 125-144.  [MR 96e:11156]  [Zbl 874.11079]

    [7] "On a class of congruences for Lucas sequences", in Applications of Fibonacci Numbers, Vol.6 (1996), G. E. Bergum et. al. ,eds., Kluwer Academic Publishers, 537-544.  [MR 97c:11025]  [Zbl 862.11017]

    [8] "Congruences for generalised Dickson polynomials", in Applications of Finite Fields, IMA Conference Series, Vol. 59 (1996), D. Gollman, ed., Oxford University Press, 33-46.  [MR 98c:11133]   [Zbl 884.11052]

    [9] "Some congruences and identities for generalizations of Rédei functions", in Finite Fields and Applications, London Mathematical Society Lecture Note Series, Vol. 233 (1996), S. Cohen and H. Niederreiter, eds., Cambridge University Press, 395-401.  [MR 97j:11064]   [Zbl 865.11082]

    [10] "Congruences for Bernoulli, Euler, and Stirling numbers", Journal of Number Theory 78.2 (1999), 204-227.  [MR 2000i:11038]  [Zbl 939.11014]

    [11] "Kummer congruences for values of Bernoulli and Euler polynomials", Acta Arithmetica 99.3 (2001), 277-288.  [MR 2002g:11021]  [Zbl 982.11008]

    [12] "On modified Dickson polynomials", The Fibonacci Quarterly 40.1 (2002), 33-40.  [MR 2003d:11034]  [Zbl 1138.11313]

    [13] "On the behavior of some two-variable p-adic L-functions", Journal of Number Theory 98.1 (2003), 67-88.  [MR 2003m:11198]  [Zbl 1067.11076]

    [14] "On lacunary recurrences", The Fibonacci Quarterly 41.1 (2003), 41-47.  [MR 2003m:11020]  [Zbl 1056.11004]

    [15] "Congruences for degenerate number sequences", Discrete  Mathematics 270 (2003), 279-289.    [MR 2004e:11016]  [Zbl 1042.11015]

    [16] "Gauss sums and multinomial coefficients" Journal of Number Theory 106.1 (2004), 13-25.  [MR 2005a:11122]  [Zbl 1052.11057]

    [17] "Degenerate and n-adic versions of Kummer's congruences for values of Bernoulli polynomials",  Discrete Mathematics 285 (2004), 289-296.  [MR 2005d:11025]  [Zbl 1046.11011]

    [18] "p-adic interpolation of the Fibonacci sequence via hypergeometric functions" (with Prerna Bihani and Wendy Sheppard), The Fibonacci Quarterly 43.3 (2005), 213-226.  [MR 2006k:11024]  [Zbl 1078.11007]

    [19] "Regular and strongly regular planar graphs"  (with Nirmala Limaye, Dinesh Sarvate, and Pantelimon Stănică), Journal of Combinatorial Mathematics and Combinatorial Computing 54 (2005), 111-127[MR 2006a:05046]  [Zbl 1084:05020]

    [20] "On Lucas-Bernoulli numbers"The Fibonacci Quarterly 44.4 (2006), 347-357.  [MR 2008d:11021] [Zbl 1190.11013]

    [21] "Degenerate Bernoulli polynomials, generalized factorial sums, and their applications", Journal of Number Theory 128.4 (2008), 738-758.  [MR 2009b:11045] [Zbl 05378823]

    [22] "A 2-adic formula for Bernoulli numbers of the second kind and for the Nörlund numbers", Journal of Number Theory 128.11 (2008), 2951-2962.  [MR 2009i:11027] [Zbl 1182.11014]

    [23] "On higher order Lucas-Bernoulli numbers" (with Kyle Keepers),  The Fibonacci Quarterly 46/47 (2008/2009), 26-31.  [MR 2010b:11025] [Zbl 05542620]

    [24] "A p-adic formula for the Nörlund numbers and for Bernoulli numbers of the second kind", Congressus Numerantium 201 (2010), 77-87.  [MR 2598349] [Zbl 05778069]

    [25] "Coincidences of Catalan and q-Catalan numbers" (with Florian Luca), INTEGERS 11.4 (2011), 495-503.

    [26] "Bernoulli numbers and generalized factorial sums", INTEGERS 11.4 (2011), 553-561.

    [27] "On p-adic multiple zeta and log gamma functions" (with Brett Tangedal), Journal of Number Theory 131.7 (2011), 1240-1257.  video abstract

    [28] "On the binary expansion of the odd Catalan numbers" (with Florian Luca), Aportaciones Matemáticas Investigación 20 (2011), 185-190.

    [29] "Some p-adic congruences for pq-Catalan numbers" (with Florian Luca), Aportaciones Matemáticas Investigación 20 (2011), 191-197.

    [30] "On the log-concavity of the degenerate Bernoulli numbers" (with Florian Luca), International Journal of Number Theory 8.3 (2012), 789-800.

    [31] "On the number of divisors of n! and of the Fibonacci numbers" (with Florian Luca), Glasnik Matematički, 47 (2012), 285-293.

    [32] "Explicit computation of Gross-Stark units over real quadratic fields" (with Brett Tangedal), Journal of Number Theory 131.3 (2013), 1045-1061.  

    [33] "Rational series for multiple zeta and log gamma functions" , Journal of Number Theory 131.12 (2013), 3995-4009.