Department of Mathematics,
University of Puerto Rico
Box 70377
San Juan, PR 00936-8377
Oficina
NCN II C-113
Horas
Programa Actual
Teléfono
(787) 764-0000 88259
E-Mail
moc.liamg@rtsacsicnarf
Educación
PhD, City University of New York, The Graduate Center,, 1998
Investigación
Geometría Algebraica
Publicaciones Representativas
(F. Castro, I. Rubio, P. Guan and R. Figueroa) On System of Linear and Diagonal Equation of degree pi + 1 over Finite Fields of Characteristic p, Finite Fields and Applications, 14, 648-657, 2008.
(F. Castro, I. Rubio and J. Vega) Divisibility of Exponential Sums and Solvability of Certain Equations over Finite Fields, Quart. J. Math., 60, 169-181, 2009.
(R. Arce, F. Castro and R. Figueroa), On the number of solutions of [latex]sum_{i=1}^{11}frac{1}{x_i}=1[/latex] in distinct odd natural numbers, J. Number Theory, 133(6), 2036-2046, 2013.
(O. Moreno, K. Shum, F. N. Castro, and P.V. Kumar) Tight Bounds for Chevalley-Warning- Ax-Katz Type Estimates, with Improved Applications, Proc. London Society 4, 201-217, 2004.
(F. Castro and C.J. Moreno) Mixed Exponential Sums, Proceeding of American Mathematical Society, 128, 2529-2537, 2000.
(O. Moreno and F. N. Castro ) Divisibility Properties for Covering Radius for Certain Cyclic Codes IEEE Trans. Inform. Theory, 49, 3299-3302, 2003.
(F. Castro, J. Janwa, G. Mullen and R. Rubio), e-Perfect Codes, Bull. Inst. Combin. Appl. 83-90, 2015.
(F. Castro, H. Randriam, I. Rubio and H.F. Mattson Jr.) Divisibility of exponential sums via elementary methods, J. Number Theory, 130(7), 1520-1536, 2010.
(F. N. Castro, (with R. A. Arce-Nazario, J. Crdova, K. Hicks, G. L. Mullen, and I. Rubio) Some computational results concerning the spectrum of sets of latin squares, Quasigroups and Related Systems 22, 159-164,2014.
(F. Castro and L. Medina) Asymptotic Behavior of Perturbations of Symmetric Functions, Annals of Combinatorics 18, 397-417, 2014.
(F. Castro and I. Rubio) Construction of systems of polynomial equations with exact p- Divisibility via the covering method, J. Algebra Appl. 13, 2014.
(F. Castro, L. Medina and Gonzlez), The p-adic Valuation of Eulerian Numbers: Trees and Bernoulli Numbers, Experimental Mathematics 24 (2), 183-195, 2015.
(F. Castro, L. Medina and O. Gonzlez) A Divisibility Approach to the Open Boundary Cases of Cusick-Li-Stnics Conjecture, Cryptography and Communications: Discrete Struc- tures, Boolean Functions and Sequences 7 (4), 183-195, 2015.
(F. Castro, H. Janwa, G. Mullen and I. Rubio) e-perfect codes. Bull. Inst. Combin. Appl. 75, 8390, 2015.
(F. Castro and I. Rubio) Exact p-Divisibility of Exponential Sums vias the Covering Methods, Proceeding of American Mathematical Society 143, 1043-1056, 2015.
(F. Castro, R. Figueroa, P. Guan and J. Ortiz-Ubarri) Divisibility of Exponential Sums Associated to binomial,Contemporary Developments in Finite Fields and Their Applications, World Scientific Press, 11-21, 2016.
(F. Castro and R. Figueroa) p-adics Valuation of Exponential Sums associated to Trinomial and Some Consequences, ¡it p-adics Number, Ultrametric Analysis and Applications 7, 257- 266, 2017.
(F. Castro, Rafael Arce-Nazario and Jose Ortiz-Ubarri) On the covering radius of some binary cyclic codes, Advances in Mathematics of Communications 11, 329-338, 2017.
(F. Castro, R. Arce-Nazario and R. Figueroa) On the Equation [latex]sum_{i=1}^{n}frac{1}{x_i}=1[/latex] in Distinct Odd or Even Numbers, Contribution to Discrete Mathematics 11, 63-78, 2017.
(F. Castro, Figueroa and R. Guan, P.) p-adic valuation of exponential sums in one variable associated to binomials, Uniform Distribution Theory 12, 37-52, 2017.
(F. N. Castro, Carlos Corrada-Bravo, Natalia Pacheco-Tallaj and Ivelisse Rubio), Explicit formulas for monomial involutions over finite fields, Advances in Mathematics of Communi- cations 11, 301-306, 2017.
(F. Castro and L. Medina) Modular periodicity of exponential sums of symmetric Boolean functions, Discrete Applied Mathematics 217, 455-473,2017.
(F. Castro, O. González, and L. Medina) Generalized Exponential Sums and the Power of the Computer, Involve 11, 127-142, 2018.