Výsledky vyhledávání - "Gregory P. Dresden"

Autor: Prakriti Panthi, Anukriti Shrestha, Jiahao Zhang, Gregory P. Dresden, Saimon Islam

Publikováno v: The American Mathematical Monthly. 127:316-329

How many irreducible polynomials have real roots which, when expressed as simple continued fractions, all have common tails? We show how to identify all such polynomials (they have degree at most s...

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https://doi.org/10.1080/00029890.2019.1704165

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Finite subgroups of the extended modular group

Autor: Prakriti Panthi, Gregory P. Dresden, Anukriti Shrestha, Jiahao Zhang

Publikováno v: Rocky Mountain J. Math. 49, no. 4 (2019), 1123-1127

We show that in the extended modular group PGL(2,Z) there are exactly seven finite subgroups up to conjugacy; three subgroups of size 2, one subgroup each of size 3, 4, and 6, and the trivial subgroup of size 1.
Comment: 4 pages; version 2 has a

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https://projecteuclid.org/euclid.rmjm/1567044031

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Three Transcendental Numbers from the Last Non-Zero Digits of nn, Fn, and n!

Autor: Gregory P. Dresden

Publikováno v: Mathematics Magazine. 81:96-105

In this article, we will construct three infinite decimals from the last nonzero digits of n n , Fn (the Fibonacci numbers), andn!, respectively, and we will show that all three are transcendental. Along the way, we will learn a bit about the history

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https://doi.org/10.1080/0025570x.2008.11953536

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A Combinatorial Proof of Vandermonde's Determinant

Autor: Arthur T. Benjamin, Gregory P. Dresden

Publikováno v: The American Mathematical Monthly. 114:338-341

(2007). A Combinatorial Proof of Vandermonde's Determinant. The American Mathematical Monthly: Vol. 114, No. 4, pp. 338-341.

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https://doi.org/10.1080/00029890.2007.11920421

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There Are Only Nine Finite Groups of Fractional Linear Transformations with Integer Coefficients

Autor: Gregory P. Dresden

Publikováno v: Mathematics Magazine. 77:211-218

(2004). There Are Only Nine Finite Groups of Fractional Linear Transformations with Integer Coefficients. Mathematics Magazine: Vol. 77, No. 3, pp. 211-218.

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https://doi.org/10.1080/0025570x.2004.11953253

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Sums of heights of algebraic numbers

Autor: Gregory P. Dresden

Publikováno v: Mathematics of Computation. 72:1487-1500

For At(x) = f(x) - tg(x), we consider the set {ΣAt(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 compu

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https://doi.org/10.1090/s0025-5718-02-01481-3

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Two Irrational Numbers From the Last Nonzero Digits of n! and nn

Autor: Gregory P. Dresden

Publikováno v: Mathematics Magazine. 74:316-320

(2001). Two Irrational Numbers From the Last Nonzero Digits of n! and nn. Mathematics Magazine: Vol. 74, No. 4, pp. 316-320.

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https://doi.org/10.1080/0025570x.2001.11953085

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On the Middle Coefficient of a Cyclotomic Polynomial

Autor: Gregory P. Dresden

Publikováno v: The American Mathematical Monthly. 111:531-533

Clearly (, has degree 0 (n), where 0 signifies Euler's totient function. These monic polynomials can be defined recursively as (I1 (x) = x 1 and Hiln D (x) = xn 1 for n > 1. The first few are easily calculated to be x 1, x + 1, x2 + x + , x2 + 1....

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https://doi.org/10.1080/00029890.2004.11920111

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