# Papers by Luis A. Medina

### Submitted

1. Closed formulas for exponential sums of symmetric polynomials over Galois fields
[With F. Castro and L. B. Sepulveda]

2. Hadamard matrices and the spectrum of quadratic symmetric polynomials over finite fields
[With F. Castro]

3. Recursions associated to trapezoid, symmetric and rotation symmetric functions over Galois fields
[With F. Castro, R. Chapman and L. B. Sepulveda]

4. 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]

### Published/to appear

1. Generalized Walsh transforms of symmetric and rotation symmetric Boolean functions are linear recurrent
[With F. Castro and P. Stanica]
To appear in Applicable Algebra in Engineering, Communication and Computing

2. Exact 2-Divisibility of Exponential Sums of Associated to Boolean Functions
[With F. Castro and I. Rubio]
To appear in Cryptography and Communications

3. 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]
To appear in Designs, Codes and Cryptography

4. 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.

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

6. Periodicity in the $$p$$-adic valuation of a polynomial
[With V. Moll and E. Rowland ]
Journal of Number Theory , 180, 2017, 139-153.

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

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

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

10. 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.

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

12. The integrals in Gradshteyn and Ryzhik. Part 27: More logarithmic examples
[With V. Moll ]
Scientia , 26, 2015, 49-61.

13. Asymptotic behavior of perturbations of symmetric functions
[With F. Castro]
Annals of Combinatorics, 18, 397-417, 2014.

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

15. 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.

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

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

18. 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.

19. 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.

20. 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.

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

22. A class of logarithmic integrals
[With V. Moll]
The Ramanujan Journal 20, 2009, 91-126.

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

24. 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.

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

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

27. 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

Luis A. Medina's homepage