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Papers by Luis A. Medina

Non-mathematical writings and unpublished notes

• The state of the Academia in Puerto Rico after hurricane Maria
  Notices of the American Mathematical Society (invited) 65(8) (2018) 964-965.

• Juracan: Guabancex's secrete wapon
  Unpublished note. Personal writing.

• Short cycle rotation Boolean functions: generators and count
  [With J. E. Calderon-Gomez, C. Molina-Salazar]

Published/to appear

38. Short k-cycle rotation Boolean functions
    [With J. E. Calderon-Gomez, C. Molina-Salazar]
    Discrete Applied Mathematics 343 (2024) 49-64.


37. Recurrences in terms of special polynomials for exponential sums of elementary symmetric polynomials over finite fields
    [With A. Gomez-Flores, L. Pomales, C. Santiago-Calderon]
    INTEGERS 23 (2023) \#A11.


36. Recursions for modified Walsh transforms of some families of Boolean functions
    [With A. O. Gomez-Flores and P. Stanica]
    Rocky Mountain J. Math. 52(4) (2022) 1355-1373.


35. Walsh-Hadamard transforms of generalized p-ary functions and C-finite sequences
    [With L. B. Sepulveda and C. Serna-Rapello]
    Discrete Applied Mathematics 315 (2022) 86-96.


34. Root-Hadamard transforms and complementary sequences
    [With M. G. Parker, C. Riera and P. Stanica]
    Cryptography and Communications 12 (2020) 1035-1049


33. Value distribution of elementary symmetric polynomials and their perturbations over finite fields
    [With L. B. Sepulveda and C. Serna-Rapello]
    Finite Fields and Their Applications 63(2) (2020) 101632


32. A closed-form solution might be given by a tree. Valuations of quadratic polynomials
    [With A. Byrnes, J. Fink, G. Lavigne, I. Nogues, S. Rajasekaran, A. Yuan, L. Almodovar, X. Guan, A. Kesarwani, E. Rowland , and V. Moll]
    Scientia, Series A: Math. Sciences 29 (2019) 11-28.


31. Closed formulas for exponential sums of symmetric polynomials over Galois fields
    [With F. Castro and L. B. Sepulveda]
    Journal Algebraic Combinatorics 50(1) (2019) 73-98.


30. An improvement to Chevalley's Theorem with restricted variables
    [With F. Castro and O. Gonzalez]
    Finite Fields and Their Applications 58 (2019) 216-221.


29. Generalized Walsh transforms of symmetric and rotation symmetric Boolean functions are linear recurrent
    [With F. Castro and P. Stanica]
    Applicable Algebra in Engineering, Communication and Computing 29(5) (2018) 433-453.


28. Recursions associated to trapezoid, symmetric and rotation symmetric functions over Galois fields
    [With F. Castro, R. Chapman and L. B. Sepulveda]
    Discrete Mathematics 341(7) (2018) 1915-1931.


27. Hadamard matrices and the spectrum of quadratic symmetric polynomials over finite fields
    [With F. Castro]
    Linear Algebra and its Applications 549 (2018) 153-175.


26. Exact 2-Divisibility of Exponential Sums of Associated to Boolean Functions
    [With F. Castro and I. Rubio]
    Cryptography and Communications 10(4) (2018) 655-666.


25. New families of balanced symmetric functions and a generalization of Cusick, Li and Stanica's conjecture
    [With R. Arce-Nazario, F. Castro, O. Gonzalez, and I. Rubio]
    Designs, Codes and Cryptography 86 (2018) 693-701.


24. Diophantine equations with binomial coefficients and perturbations of symmetric Boolean functions
    [With F. Castro and O. Gonzalez]
    IEEE Trans. Inf. Theory 64(2) (2018) 1347-1360.


23. Generalized exponential sums and the power of computers
    [With F. Castro and O. Gonzalez]
    Involve 11(1) (2018) 127-142.


22. Periodicity in the \(p\)-adic valuation of a polynomial
    [With V. Moll and E. Rowland ]
    Journal of Number Theory 180 (2017) 139-153.


21. Modular periodicity of exponential sums of symmetric Boolean functions and some of its consequences
    [With F. Castro]
    Discrete Applied Mathematics 217 (2017) 455-473.


20. On multiple and infinite log-concavity
    [With A. Straub ]
    Annals of Combinatorics 20 (1) (2016) 125-138.


19. p-regularity of the p-adic valuation of the Fibonacci sequence
    [With E. Rowland ]
    The Fibonacci Quarterly 53 (3) (2015) 265-271.


18. A divisibility approach to the open boundary cases of Cusick-Li-Stanica's conjecture
    [With F. Castro and O. Gonzalez]
    Cryptography and Communications 7 (4) (2015) 379-402.


17. The p-adic valuation of Eulerian numbers: trees and Bernoulli numbers
    [With F. Castro and O. Gonzalez]
    Experimental Mathematics 24 (2) (2015) 183-195.


16. The integrals in Gradshteyn and Ryzhik. Part 27: More logarithmic examples
    [With V. Moll ]
    Scientia, Series A: Math. Sciences 26 (2015) 49-61.


15. Asymptotic behavior of perturbations of symmetric functions
    [With F. Castro]
    Annals of Combinatorics 18 (2014) 397-417.


14. The integrals in Gradshteyn and Ryzhik. Part 23: Combination of logarithms and rational functions
    [With V. Moll ]
    Scientia, Series A: Math. Sciences 23 (2012) 1-18.


13. Exact Divisibility of Exponential Sums and Some Consequences
    [With F. Castro and R. Figueroa]
    Theory and Applications of Finite Fields, Contemporary Mathematics 579 (2012) 55-66.


12. Iterated primitives of logarithmic powers
    [With V. Moll and E. Rowland ]
    International Journal of Number Theory 7(3) (2011) 623-634.


11. Linear Recurrences and Asymptotic Behavior of Exponential Sums of Symmetric Boolean Functions
    [With F. Castro]
    Elec. J. Combinatorics 18(2) (2011), #P8.


10. Exact Divisibility of Exponential Sums over the Binary Field via the Covering Method
    [With F. Castro and I. Rubio ]
    Groups, Algebras and Applications, Contemporary Mathematics 537 (2011) 129-136.


9. The p-adic valuation of Stirling numbers
   [With A. Berrizbeitia, A. Moll, V. Moll, and L. Noble]
   Journal for Algebra and Number Theory Academia 1 (2010) 1-30.
   
   Note: Ana Berrizbeitia, Alexander Moll and Laine Noble were undergraduate students at the time this research was done.


8. An Experimental Mathematics Perspective on the Old, and still Open, Question of When To Stop?
   [With D. Zeilberger]
   Gems in Experimental Mathematics, Contemporary Mathematics 517 (2010) 265-274.


7. A fast numerical algorithm for the integration of rational functions.
   [With D. Manna, V. Moll and A. Straub]
   Numerische Mathematik 115 (2010) 289-307.


6. A class of logarithmic integrals
   [With V. Moll]
   The Ramanujan Journal 20 (2009) 91-126.


5. Asymptotic valuations of sequences satisfying first order recurrences
   [With T. Amdeberhan and V. Moll]
   Proc. Amer. Math. Soc. 137 (2009) 885-890.


4. The integrals in Gradshteyn and Ryzhik. Part 11: The incomplete beta function
   [With K. N. Boyadzhiev and V. Moll]
   Scientia, Series A: Math. Sciences 18 (2009) 61-75.


3. The integrals in Gradshteyn and Ryzhik. Part 10: The digamma function
   [With V. Moll]
   Scientia, Series A: Math. Sciences 17 (2009) 45-66.


2. Arithmetical properties of a sequence arising from an arctangent sum
   [With T. Amdeberhan and V. Moll]
   Journal of Number Theory 128 (2008) 1808-1847.


1. The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals
   [With T. Amdeberhan and V. Moll ]
   Scientia, Series A: Math. Sciences 15 (2007) 47-60.

Papers in arXiv

• Papers in arXiv.org