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.
"Symmetries of Stirling Number Series", Sixteenth International
Conference on Fibonacci Numbers and their Applications, 2014.
"The p-adic Arakawa-Kaneko Zeta Functions and p-adic
Lerch Transcendent", West Coast Number Theory Conference, 2014.
[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.
[34] "Symmetries of Bernoulli polynomial
series and Arakawa-Kaneko zeta functions" , Journal of
Number Theory 143
(2014), 142-161.