Francis N. Castro

Address College of Natural Sciences
Department of Mathematics
17 University Ave. Ste 1701
San Juan, PR 00925-2537
Office NCN II C-113
Office Hours
Program
Telephone (787) 764-0000 88259
E-Mail moc.liamg@rtsacsicnarf
MathSciNet Link

Education

PhD, City University of New York, The Graduate Center,, 1998

Research

Algebraic geometry; number theory

Selected Publications

  1. (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.
  2. (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.
  3. (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.
  4. (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.
  5. (F. Castro and C.J. Moreno) Mixed Exponential Sums, Proceeding of American Mathematical Society, 128, 2529-2537, 2000.
  6. (O. Moreno and F. N. Castro ) Divisibility Properties for Covering Radius for Certain Cyclic Codes IEEE Trans. Inform. Theory, 49, 3299-3302, 2003.
  7. (F. Castro, J. Janwa, G. Mullen and R. Rubio), e-Perfect Codes, Bull. Inst. Combin. Appl. 83-90, 2015.
  8. (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.
  9. (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.
  10. (F. Castro and L. Medina) Asymptotic Behavior of Perturbations of Symmetric Functions, Annals of Combinatorics 18, 397-417, 2014.
  11. (F. Castro and I. Rubio) Construction of systems of polynomial equations with exact p- Divisibility via the covering method, J. Algebra Appl. 13, 2014.
  12. (F. Castro, L. Medina and Gonzlez), The p-adic Valuation of Eulerian Numbers: Trees and Bernoulli Numbers, Experimental Mathematics 24 (2), 183-195, 2015.
  13. (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.
  14. (F. Castro, H. Janwa, G. Mullen and I. Rubio) e-perfect codes. Bull. Inst. Combin. Appl. 75, 8390, 2015.
  15. (F. Castro and I. Rubio) Exact p-Divisibility of Exponential Sums vias the Covering Methods, Proceeding of American Mathematical Society 143, 1043-1056, 2015.
  16. (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.
  17. (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.
  18. (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.
  19. (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.
  20. (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.
  21. (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.
  22. (F. Castro and L. Medina) Modular periodicity of exponential sums of symmetric Boolean functions, Discrete Applied Mathematics 217, 455-473,2017.
  23. (F. Castro, O. González, and L. Medina) Generalized Exponential Sums and the Power of the Computer, Involve 11, 127-142, 2018.

Selected Grants and Awards

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