#### Filter Results:

#### Publication Year

1998

2009

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

We offer a combinatorial method of evaluating Vandermonde's determinant,

In this paper, we present a particularly nice Binet-style formula that can be used to produce the k-generalized Fibonacci numbers (that is, the Tribonaccis, Tetranaccis, etc.). Furthermore, we show that in fact one needs only take the integer closest to the first term of this Binet-style formula in order to generate the desired sequence.

We prove that the two smallest values of h(α)+h(1 1−α)+h(1− 1 α) are 0 and 0.4218. .. , for α any algebraic integer.

The cyclotomic polynomials n for n = 1, 2, 3,. .. (familiar to every student of algebra) are the minimal polynomials for the primitive nth roots of unity: n (x) = (k,n)=1 x − e 2πik/n. Clearly n has degree φ(n), where φ signifies Euler's totient function. These monic polynomials can be defined recursively as 1 (x) = x − 1 and i|n i (x) = x n − 1 for n > 1.… (More)

- Charles Lloyd Samuels, Jeffrey D. Vaaler, John Tate, Fernando Rodriguez-Villegas, Felipe Voloch, Gregory Dresden
- 2007

Acknowledgments I would like to thank my committee members, Gregory Dresden, Fer-nando Rodriguez-Villegas, John Tate and Felipe Voloch, for reviewing this dissertation and helping to make it complete. In particular, I thank Fernando Rodriguez-Villegas as well as John Garza for their ideas that inspired me to prove the results that appear here. I also thank… (More)

For At(x) = f (x) − t g(x), we consider the set { At(α)=0 h(α) : t ∈ Q}. The polynomials f (x), g(x) are in Z[x], with only mild restrictions, and h(α) is the Weil height of α. We show that this set is dense in [d, ∞) for some effectively computable limit point d.

- ‹
- 1
- ›