Welcome!

This is the personal website of Armin Straub.

I'm a graduate student of mathematics at Tulane University, New Orleans. My PhD advisor is Victor H. Moll, and my research area is an exciting mix of combinatorics, special functions and computer algebra. Recently, this has also touched some mathematical physics.

Date: Jan 7, 2012

Symbolic evaluation of log-sine integrals in polylogarithmic terms

Date: 
2012-01-07
Occasion: 
AMS Joint Meetings 2012 (Boston)

This talk, given at the AMS Joint Meetings 2012 in Boston, basically is a short version of the talk given at ISSAC 2011 and presents results of the paper Special values of generalized log-sine integrals together with a brief indication of two applications of log-sine integrals (Mahler measure and inverse binomial sums).

Abstract

Slides: 
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2012logsine-jmm.pdf
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Date: Oct 7, 2011

Hypergeometric evaluations of the densities of short random walks

Date: 
2011-10-06
Occasion: 
SIAM Conference on Applied Algebraic Geometry, Minisymposium on Symbolic Combinatorics (North Carolina State University)

We consider random walks in the plane which consist of n steps of fixed length each taken into a uniformly random direction. Our interest lies in the probability density function of the distance travelled by such a walk. While Lord Rayleigh's limiting density is an excellent approximation for moderately large n, we seek closed forms for the densities in the case of small n. read more »

Slides: 
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2011densities-ag11.pdf

Mahler measures, short walks and log-sine integrals

This is a preprint by Jonathan M. Borwein and Armin Straub.

Abstract

The Mahler measure of a polynomial in several variables has been a subject of much study over the past thirty years — very few closed forms are proven but more are conjectured. In the case of multiple Mahler measures more tractable but interesting families exist. Using values of log-sine integrals we provide systematic evaluations of various higher and multiple Mahler measures. read more »

Download:
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walksmahlerlogsin.pdf

A Sinc that Sank

This article by David Borwein, Jonathan M. Borwein and Armin Straub has been published in American Mathematical Monthly (to appear).

Abstract

We resolve and further study a sinc integral evaluation, first posed in the American Mathematical Monthly in [1967, p. 1015], which was solved in [1968, p. 914] and withdrawn in [1970, p. 657]. After a short introduction to the problem and its history, we give a general evaluation which we make entirely explicit in the case of the product of three sinc functions. Finally, we exhibit some general structure of the integrals in question.

Download:
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sinc-sank.pdf
Date: Aug 24, 2011

q-binomial coefficient congruences

Date: 
2011-08-23
Occasion: 
CARMA Analysis and Number Theory Seminar (University of Newcastle)

In the first part of this talk the q-binomial coefficients are introduced in a variety of different ways in order to demonstrate that they are a very natural and beautiful generalization of the usual binomial coefficients. Having thus established that they are interesting objects in their own right, we consider several classical congruences for binomial coefficients with the objective of extending them to the q-world. In this second part of the talk results from the paper A q-analog of Ljunggren's binomial congruence are included.

Slides: 
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2011qanalogs-carma.pdf
Date: Jul 13, 2011

A Sage package for evaluating log-sine integrals

This Sage package accompanies the paper Special values of generalized log-sine integrals.

Besides the package you find a notebook which shows basic usage. If you don't have access to Sage you can still look at the attached pdf file logsine-sage-usage.pdf which illustrates the package in use.

Note that the package is preliminary and has several rough edges—please report any issues to math@arminstraub.com. Integration into the core of Sage is a hoped for possibility. read more »

Attachment: 
application/octet-stream icon
logsine.sage
application/octet-stream icon
logsine-sage-usage.sws
application/pdf icon
logsine-sage-usage.pdf
in
Date: Jun 10, 2011

Special Values of Generalized log-sine Integrals

Date: 
2011-06-09
Occasion: 
ISSAC 2011 (San Jose, CA)

This talk is presenting the paper Special values of generalized log-sine integrals at ISSAC 2011 which stands for International Symposium on Symbolic and Algebraic Computation.

The presentation was similar to the one given at JonFest a few weeks ago but focused a bit more on the actual evaluations of log-sine integrals and was more sketchy when it came to applications. read more »

Slides: 
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2011logsine-issac.pdf

Ramanujan's Master Theorem

This article by Tewodros Amdeberhan, Ivan Gonzalez, Marshall Harrison, Victor H. Moll and Armin Straub has been published in The Ramanujan Journal (to appear).

Abstract

S. Ramanujan introduced a technique, known as Ramanujan's Master Theorem, which provides an explicit expression for the Mellin transform of a function in terms of the analytic continuation of its Taylor coefficients. The history and proof of this result are reviewed, and a variety of applications is presented. Finally, a multi-dimensional extension of Ramanujan's Master Theorem is discussed.

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application/pdf icon
rmt.pdf
Date: May 20, 2011

Applications and evaluations of log-sine integrals

Date: 
2011-05-19
Occasion: 
JonFest 2011: Workshop on Computational and Analytical Mathematics in honour of Jonathan Borwein's 60th birthday (Simon Fraser University, CA)

It was my pleasure to give this talk at JonFest 2011 in honour of Jon's 60th birthday. After the first part of the talk tries to give a nontechnical overview of our results on the evaluation of log-sine integrals, the second part shortly highlights various applications of such evaluations and connects the topic with our previous research on random walks and Mahler measures.

Abstract

Slides: 
application/pdf icon
2011logsine-jonfest.pdf
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