University of Puerto Rico    (787) 764 0000

    Professor Information

    Luis A. Medina

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

    Education

    Ph.D., Tulane University, 2008

    Research Interests

    Matemática Experimental. Teoría de Números. Funciones Especiales.

    Selected Publications

    1. Luis A. Medina, L. Brehsner Sepulveda and Cesar Serna-Rapello. Value distribution of elementary symmetric polynomials and their perturbations over finite fields. Finite Fields and Their Applications 63(2) (2020) 1-21.
    2. A closed-form solution might be given by a tree. Valuations of quadratic polynomials. Authors: A. Byrnes, J. Fink, G. Lavigne, I. Nogues, S. Rajasekaran, A. Yuan, L. Almodovar, X. Guan, A. Kesarwani, Luis A. Medina, E. Rowland , and V. Moll. Scientia, Series A: Math. Sciences 29 (2019) 11-28.
    3. Closed formulas for exponential sums of symmetric polynomials over Galois fields. Authors: F. Castro, L. A. Medina and L. B. Sepulveda. Journal of Algebraic Combinatorics 50(1) (2019) 73-98.
    4. An improvement to Chevalley’s Theorem with restricted variables, Authors: Francis N. Castro, Oscar E. González and Luis A. Medina; Finite Fields and Their Applications, 58, 2019, 216-221.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Modular periodicity of exponential sums of symmetric Boolean functions, Authors: Luis A. Medina and Armin Straub; Discrete Appl. Math., 217, 2017, 455–473.
    12. On multiple and infinite log-concavity, Authors: Luis A. Medina and Armin Straub; Annals of Combinatorics, 20(1), 2016, 125-138.
    13. The integrals in Gradshteyn and Ryzhik. Part 27: More logarithmic examples, Authors: Luis A. Medina and Victor H. Moll; Scientia, 26, 2015, 49-61.
    14. 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.
    15. 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.
    16. 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.
    17. Asymptotic Behavior of Perturbations of Symmetric Functions, Authors: Francis Castro and Luis A. Medina; Annals of Combinatorics, 18, 397-417, 2014.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. A Class of Logarithmic Integrals, Authors: Luis A. Medina and Victor H. Moll; The Ramanujan Journal 20, 2009, 91-126.
    27. 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.
    28. 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.
    29. 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.
    30. 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.
    31. 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.

    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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