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Papers by Luis A. Medina
Non-mathematical writings
The state of the Academia in Puerto Rico after hurricane Maria
To appear in
Notices of the American Mathematical Society
(invited)
Juracan: Guabancex's secrete wapon
Unpublished note. Personal writing.
Submitted
An improvement to Chevalley's Theorem with restricted variables
[With F. Castro and O. Gonzalez]
Closed formulas for exponential sums of symmetric polynomials over Galois fields
[With F. Castro and L. B. Sepulveda]
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
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
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.
Hadamard matrices and the spectrum of quadratic symmetric polynomials over finite fields
[With F. Castro]
Linear Algebra and its Applications
,
549
, 2018, 153-175.
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.
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.
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.
Generalized exponential sums and the power of computers
[With F. Castro and O. Gonzalez]
Involve
,
11(1)
, 2018, 127-142.
Periodicity in the \(p\)-adic valuation of a polynomial
[With
V. Moll
and E. Rowland ]
Journal of Number Theory
,
180
, 2017, 139-153.
Modular periodicity of exponential sums of symmetric Boolean functions and some of its consequences
[With F. Castro]
Discrete Applied Mathematics
,
217
, 2017, 455-473.
On multiple and infinite log-concavity
[With
A. Straub
]
Annals of Combinatorics
,
20 (1)
, 2016, 125-138.
p-regularity of the p-adic valuation of the Fibonacci sequence
[With
E. Rowland
]
The Fibonacci Quarterly
,
53 (3)
, 2015, 265-271.
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.
The p-adic valuation of Eulerian numbers: trees and Bernoulli numbers
[With F. Castro and O. Gonzalez]
Experimental Mathematics
,
24 (2)
, 2015, 183-195.
The integrals in Gradshteyn and Ryzhik. Part 27: More logarithmic examples
[With V. Moll ]
Scientia
,
26
, 2015, 49-61.
Asymptotic behavior of perturbations of symmetric functions
[With F. Castro]
Annals of Combinatorics
,
18
, 397-417, 2014.
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.
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.
Iterated primitives of logarithmic powers
[With
V. Moll
and
E. Rowland
]
International Journal of Number Theory
,
7 (3)
, 2011, 623-634.
Linear Recurrences and Asymptotic Behavior of Exponential Sums of Symmetric Boolean Functions
[With F. Castro]
Elec. J. Combinatorics
,
18(2)
(2011), #P8.
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.
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.
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.
A fast numerical algorithm for the integration of rational functions.
[With D. Manna,
V. Moll
and A. Straub]
Numerische Mathematik
,
115
, 2010, 289-307.
A class of logarithmic integrals
[With
V. Moll
]
The Ramanujan Journal
20
, 2009, 91-126.
Asymptotic valuations of sequences satisfying first order recurrences
[With
T. Amdeberhan
and
V. Moll
]
Proc. Amer. Math. Soc.
137
, 2009, 885-890.
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.
The integrals in Gradshteyn and Ryzhik. Part 10: The digamma function
[With
V. Moll
]
Scientia
, Series A: Math. Sciences
17
, 2009, 45-66.
Arithmetical properties of a sequence arising from an arctangent sum
[With
T. Amdeberhan
and
V. Moll
]
Journal of Number Theory
128
, 2008, 1808-1847.
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
Luis A. Medina's homepage