Luis A. Medina

Address College of Natural Sciences
Department of Mathematics
17 University Ave. Ste 1701
San Juan, PR 00925-2537
Office NCN II A-109
Office Hours
Program
Telephone (787) 764-0000 88249
E-Mail ude.rpu@71anidem.siul
MathSciNet Link

Education

Ph.D., Tulane University, 2008

Research

Experimental Math, Number Theory, Special Functions.

Selected Publications

  1. Generalized Walsh transforms of symmetric and rotation symmetric Boolean functions are linear recurrent, Authors: Francis N. Castro, Luis A. Medina and Pantelimon Stannic; To appear in Applicable Algebra in Engineering, Communication and Computing.
  2. Exact 2-Divisibility of Exponential Sums Associated to Boolean Functions, Authors: Francis N. Castro, Luis A. Medina and Ivelisse Rubio; To appear in Cryptography and Communications.
  3. New families of balanced symmetric functions and a generalization of Cusick, Li and Stănică’s conjecture, Authors: R. Arce-Nazario, F. N. Castro, O. E. González, L. A. Medina, and I. Rubio; To appear in Designs, Codes and Cryptography.
  4. Diophantine equations with binomial coefficients and perturbations of symmetric Boolean functions, Authors: Francis N. Castro, Oscar E. González and Luis A. Medina; IEEE Trans. Inf. Theory, 64(2), 2018, 1347–1360.
  5. Generalized exponential sums and the power of computers, Authors: Francis N. Castro, Oscar E. González and Luis A. Medina; Involve, 11(1), 2018, 127–142.
  6. Periodicity in the p-adic valuation of a polynomial Authors: Luis A. Medina, Victor H. Moll and Eric S. Rowland; The Journal of Number Theory, 180, 2017, 139–153.
  7. Modular periodicity of exponential sums of symmetric Boolean functions, Authors: Luis A. Medina and Armin Straub; Discrete Appl. Math., 217, 2017, 455–473.
  8. On multiple and infinite log-concavity, Authors: Luis A. Medina and Armin Straub; Annals of Combinatorics, 20(1), 2016, 125-138.
  9. The integrals in Gradshteyn and Ryzhik. Part 27: More logarithmic examples, Authors: Luis A. Medina and Victor H. Moll; Scientia, 26, 2015, 49-61.
  10. p-regularity of the p-adic valuation of the Fibonacci sequence Authors: Luis A. Medina and Eric S. Rowland; The Fibonacci Quarterly, 53 (3), 2015, 265-271.
  11. A divisibility approach to the open boundary cases of Cusick-Li-Stănică’s Conjecture Authors: Francis Castro, Oscar E. González and Luis A. Medina; Cryptography and Communications, 7 (4), 2015, 379-402.
  12. The p-adic valuation of Eulerian numbers: trees and Bernoulli numbers Authors: Francis Castro, Oscar E. González and Luis A. Medina; Experimental Mathematics, 24 (2), 2015, 183-195.
  13. Asymptotic Behavior of Perturbations of Symmetric Functions, Authors: Francis Castro and Luis A. Medina; Annals of Combinatorics, 18, 397-417, 2014.
  14. The integrals in Gradshteyn and Ryzhik. Part 23: Combination of logarithms and rational functions, Authors: Luis A. Medina and Victor H. Moll; Scientia, Series A: Math. Sciences 23, 2012, 1-18.
  15. Exact Divisibility of Exponential Sums and Some Consequences, Authors: Francis N. Castro, Luis A. Medina, and Rau ́l Figueroa; Theory and Applications of Finite Fields, AMS Contemporary Math., 579, 2012, 55-66.
  16. Iterated primitives of logarithmic powers, Authors: Luis A. Medina, Victor H. Moll and Eric S. Rowland; International Journal of Number Theory, 7, Num. 3, 2011.
  17. Linear Recurrences and Asymptotic Behavior of Exponential Sums of Symmetric Boolean Functions, Authors: Francis N. Castro and Luis A. Medina; Elec. J. Combinatorics, 18(2), 2011, #P8.
  18. Exact Divisibility of Exponential Sums over the Binary Field via the Covering Method, Authors: Francis N. Castro, Luis A. Medina and Jvelisse Rubio; Groups, Algebras and Applications, AMS Contemporary Math., 537, 2011, 129-136.
  19. The p-adic valuation of Stirling numbers, Authors: A. Berrizbeitia, L. Medina, A. Moll, V. Moll, and L. Noble; Journal for Algebra and Number Theory Academia, 1, 2010, 1-30.
  20. An Experimental Mathematics Perspective on the Old, and still Open, Question of When To Stop?, Authors: Luis A. Medina and Doron Zeilberger; Gems in Experimental Mathematics, AMS Contemporary Math. 517, 2010, 265-274.
  21. A fast numerical algorithm for the integration of rational functions, Authors: Dante Manna, Luis A. Medina, Victor H. Moll, and Armin Straub; Numerische Mathematik 115, 2010, 289-307.
  22. A Class of Logarithmic Integrals, Authors: Luis A. Medina and Victor H. Moll; The Ramanujan Journal 20, 2009, 91-126.
  23. Asymptotic valuations of sequences satisfying first order recurrences, Authors: Tewodros Amdeberhan, Luis A. Medina, and Victor H. Moll; Proc. Amer. Math. Soc. 137, 2009, 885-890.
  24. Arithmetical properties of a sequence arising from an arctangent sum, Authors: Tewodros Amdeberhan, Luis A. Medina, and Victor H. Moll; Journal of Number Theory 128, 2008, 1808-1847.
  25. The integrals in Gradshteyn and Ryzhik. Part 11: The incomplete beta function, Authors: Khristo N. Boyadzhiev, Luis A. Medina, and Victor H. Moll; Scientia, Series A: Math. Sciences 18, 2009, 61-75.
  26. The integrals in Gradshteyn and Ryzhik. Part 10: The digamma function, Authors: Luis A. Medina and Victor H. Moll; Scientia, Series A: Math. Sciences 17, 2009, 45-66.
  27. The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals, Authors: Tewodros Amdeberhan, Luis A. Medina, and Victor H. Moll Scientia, Series A: Math. Sciences 15, 2007, 47-60.

Selected Grants and Awards

  1. Scholarship fund for excellence in Computer Science and Mathematics NSF DUE-1356474 (Co-PI), 2014 - 2019. Amount: $630,217.00
  2. Computerized Pure Mathematics: Exponential Sums of Symmetric Boolean Functions Fondo Institucional para la Investigación (PI), 2014 - 2016: Amount: $36,130.00

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