Antonio
R. Vargas

Ph.D. Student

Chase Building, Room 226

Department of Mathematics and Statistics

Dalhousie University

Halifax, Nova Scotia, B3H 4J5

antoniov (at) mathstat (dot) dal (dot) ca

My CV.

I'm also on Math.StackExchange:

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Research Interests

I'm primarily interested in studying the zeros of polynomials of a single complex variable (locating them, counting them, examining asymptotic distributions in families, etc.) from the standpoint of classical analysis.

Papers

Limit curves for zeros of sections of exponential integrals

A. R. Vargas

Constructive Approximation, 40 (2014), No. 2, pp. 219-239.

[SpringerLink, arXiv]

Zeros and convergent subsequences of Stern polynomials

A. R. Vargas

Journal of Mathematical Analysis and Applications, 398 (2013), No. 2, pp. 630–637.

[ScienceDirect, arXiv]

Interlacing and non-orthogonality of spectral polynomials for the Lamé operator

A. Bourget, T. McMillen, and A. R. Vargas

Proceedings of the American Mathematical Society, 137 (2009), No. 5, pp. 1699–1710.

[AMS, arXiv]

MSc. Thesis

Zeros of Sections of Some Power Series

[arXiv]

Misc. Notes

23 Feb, 2014 | On calculating a "Mathematically Correct Breakfast", a post about the surface area exposed after cutting a bagel into two interlocking rings |

18 Feb, 2013 | An animation of the zeros of sections of exponential integrals, an interesting plot that relates to my master's thesis |

25 July, 2011 | Asymptotic bound for a particular sum, answering a question of Qiaochu Yuan |

Background

I received my BA in mathematics from California State University, Fullerton and my MSc. in mathematics from Dalhousie University.

Some cool web pages

The Beauty of Roots

John Baez

http://math.ucr.edu/home/baez/roots/

Some cool papers by other people

A sum over the zeros of partial sums of exp(x)

C. Yalçin Yildirim

Ramanujan Mathematical Society, 6 (1991), No. 1-2, pp. 51-66.

[pdf]

On the number of distinct zeros of polynomials

M. S. Klamkin and D. J. Newman

The American Mathematical Monthly, 66 (1959), No. 6, pp. 494-496.

[JSTOR]

Finite Calculus: A Tutorial for Solving Nasty Sums

David Gleich

[pdf]

Some cool books

Marden, Geometry of Polynomials

de Bruijn, Asymptotic Methods in Analysis

Halmos, Naive Set Theory

Olds, Continued Fractions