Information
on this Side of the Page:
Research Interests:
Number Theory, including Analytic, Classical Algebraic,
Combinatorial,
Computational, Elementary, and Transcedence topics. I have particular
interests in
results associated with lattice points close to (or on) a curve or
surface,
the distribution of special sequences of integers in short intervals,
applications of Pade approximations to Number Theory, the
irreducibility of polynomials over the rationals, computations with
sparse or lacunary polynomials, and covering systems of the integers.
Preprints (for published papers see "Publications" at left):
| [1] |
Laguerre polynomials with Galois group A_m for each m
, with Travis Kidd and Ognian Trifonov, submitted. |
|
Preprint:
[pdf] |
Abstract:
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| [2] |
On the factorization of consecutive integers
, with Michael Bennett and Ognian Trifonov, submitted. |
|
Preprint:
[pdf] |
Abstract:
[gif] |
| [3] |
Yet another generalization of the Ramanujan-Nagell equation
, with Michael Bennett and Ognian Trifonov, submitted. |
|
Preprint:
[pdf] |
Abstract:
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| [4] |
On powers associated with Sierpinski numbers, Riesel numbers and Polignac's conjecture
, with Carrie Finch and Mark Kozek, submitted. |
|
Preprint:
[pdf] |
Data From Tables:
[data] |
Abstract:
[gif] |
| [5] |
Irreducibility and greatest common divisor algorithms for sparse polynomials
, with Andrew Granville and Andrzej Schinzel, submitted. |
|
Preprint:
[pdf] |
Abstract:
[gif] |
| [6] |
Sieving by large integers and covering systems of congruences
with Kevin Ford, Sergei Konyagin, Carl Pomerance, and Gang Yu,
Journal of the American Mathematical Society, to appear |
|
Preprint:
[pdf] |
Abstract:
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| [7] |
T. N. Shorey's influence in the theory of irreducible polynomials ,
with Carrie Finch and J Russell Leidy,
Proceedings of the Diophantine Conference in Honor of T. N. Shorey, to appear.
|
|
Preprint:
[pdf] |
Abstract:
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| [8] |
On the irreducibility of a truncated
binomial expansion with
Angel Kumchev and Dmitrii Pasechnik, Rocky Mountain Journal of
Math., to appear. |
|
Preprint:
[pdf] |
Abstract:
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| [9] |
On three questions concerning 0,1-polynomials,
with Carrie Finch and Charles Nicol, Journal de Theorie des Nombres de Bordeaux, to appear. |
|
Preprint:
[pdf] |
Abstract:
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| [10] |
Galois groups of polynomials arising from circulant matrices,
with Florian Luca, Pante Stanica, and Robert Underwood,
Journal of Number Theory, to appear.
|
|
Preprint:
[pdf] |
Abstract:
[gif] |
| [11] |
Two Diophantine approaches to the irreducibility of certain trinomials,
with Florian Luca, Pante Stanica, and Robert Underwood,
Acta Arithmetica, to appear.
|
|
Preprint:
[pdf] |
Abstract:
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