Arithmetic of abelian varieties; Modular curves and Automorphic forms;
Elementary Number Theory, Algebraic number theory; Geometry of Physics
The worst cases for Euclidean Algorithm, submitted
Zeckendorf theorems for real numbers , submitted
Terminal digits under Zeckendorf expansion, Mathematical Communications 30 (2025), 221-229
(paper) (Joint work with Samuel Aguilar) The 3rd order Zeckendorf expansions, The Fibonacci Quarterly, 1–19. https://doi.org/10.1080/00150517.2025.2494794; Publisher's Link
(Paper) Expansions of positive integers in terms of Fibonacci terms with equally-spaced indices, to appear in Elemente der Mathematik.
Arxiv Version: The Chung-Graham Expansion (PDF)
(paper) (Joint work with Stephen J. Miller) Benford's Law under Zeckendorf expansion, the Fibonacci Quarterly 63:2, 304 - 335
(Paper) Distribution of Zeckendorf expressions, Integers 25, A25 (2025), Publisher's view
2022 (Paper) Unlikely leading digits of powers of 2, Elemente der Mathematik 78 (2023) 77-81
2022 (Paper) The Fibonacci sequence and an elliptic curve, Journal de Theorie de Nombres des Bordeaux 44 (2022)
2021 (Paper) The weak converse of Zeckendorf's Theorem, Research in Number Theory 7, Article number: 48 (2021), DOI, Publisher's View Only Link
2021 (Paper) The Space of Convolution Identities on Divisor Functions, The Ramanujan Journal 54 (2021) 650 - 677, DOI
2020 (Paper) Complex Multiplication of Two Eta Products, Colloquium Mathematicum 159 (2020) 7 - 24, DOI
(Paper) Generalization of Heronian Triples, In revision
2019 (Paper) Direct parametrization of Pythagorean triples, Notes on Number Theory and Discrete Mathematics 25 (2019) 21 - 35 YouTube
2018 (Paper) Average Number of Zeckendorf’s Integers, Journal of Number Theory 186 (2018) 452-472 JNT YouTube, DOI
2018 (Paper) Generalized Vandermonde Matrix, Pi Mu Epsilon Journal 14 (Fall 2018)
2017 (Paper) An Upper Bound on Picard Iterates, Pi Mu Epsilon Journal 14 (Fall 2017) YouTube
2012 (Solution) The solution of #941 proposed by Ovidui Furdui, Romania, The College Mathematics Journal, 43 (2012, Jan) YouTube
2011 (Filler Item) A lesson on derivatives, The American Mathematical Monthly, 119 (2012) YouTube
2009 (Animation) Taylor Polynomials Approximated by Interpolations, Wolfram Demonstrations. YouTube
2008 (Paper) Quadratic twists of an elliptic curve with small Selmer rank, Acta Arithmetica 141 (2010) 345–367. YouTube, DOI
2005 (Paper) On the arithmetic of twists of superelliptic curves, Acta Arithmetica 124 (2006) 371–389. [AMS Review] YouTube, DOI
2005 (Paper) Note on the rank of quadratic twists of Mordell equations, J. Number Theory 118 (2006) 53–61. [AMS Review] YouTube, DOI
2003 (Technical Report): Implementation of the 3-descent on a Mordell’s elliptic curve.