Related papers: Rejoinder
In this paper we introduce a class of mathematical objects called \emph{extensors} and develop some aspects of their theory with considerable detail. We give special names to several particular but important cases of extensors. The…
A survey of work on motivic integration.
Preliminary version of Chapter 2 in the book "Encyclopedia of Special functions: The Askey-Bateman Project, Vol. 2: Multivariate special functions", T. H. Koornwinder and J. V. Stokman (eds.), Cambridge University Press, 2021.
Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…
We study a continued fraction due to Ramanujan, that he recorded as Entry 12 in Chapter 16 of his second notebook. It is presented in Part III of Berndt's volumes on Ramanujan's notebooks. We give two alternate approaches to proving…
A survey article for AMS Summer Institute at Seattle in 2005.
We establish a link between the basic properties of the discriminant of periodic second-order differential equations and an elementary analysis of Herglotz functions. Some generalizations are presented using the language of self-adjoint…
Rejoinder to "Statistical Modeling of Spatial Extremes" by A. C. Davison, S. A. Padoan and M. Ribatet [arXiv:1208.3378].
This paper introduces a framework for incorporating prior information into the design of sequential experiments. These sources may include past experiments, expert opinions, or the experimenter's intuition. We model the problem using a…
Supplementary Material for "Estimation of a Multiplicative Correlation Structure in the Large Dimensional Case"
Objective priors for sequential experiments are considered. Common priors, such as the Jeffreys prior and the reference prior, will typically depend on the stopping rule used for the sequential experiment. New expressions for reference…
We introduce concepts of "recursive polynomial remainder sequence (PRS)" and "recursive subresultant," and investigate their properties. In calculating PRS, if there exists the GCD (greatest common divisor) of initial polynomials, we…
We give a simple proof of some explicit formulas of periodic continuants by Chebyshev polynomials of the second kind given by Rozsa.
A simple new proof of the Harish-Chandra condition, preceded by an expository part on Hermitian symmetric spaces, holomorphic induction, and on some analytic tools.
We consider expansions of vectors by a general class of multidimensional continued fraction algorithms. If the expansion is eventually periodic, then we describe the possible structure of a matrix corresponding to the repetend, and use it…
This is a submission to the Encyclopedia of Mathematical Physics (Elsevier, 2006) and conforms to its referencing guidelines.
These are notes for an advanced course given at Ben Gurion University in Spring 2012.
This work introduces a companion reproducible paper with the aim of allowing the exact replication of the methods, experiments, and results discussed in a previous work [5]. In that parent paper, we proposed many and varied techniques for…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
Index of notation added. Shortening of some section, simplification of some of the arguments, some small added results and strengthening of thm 3.10. Also a significant re-writing of the last section.