Related papers: Selberg Integrals
This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier.
This is a submission to the Encyclopedia of Mathematical Physics (Elsevier, 2006) and conforms to its referencing guidelines.
In this paper, we introduce a class of infinite matrices related to the Beurling algebra of periodic functions, and we show that it is an inverse-closed subalgebra of ${\mathcal B}(\ell^q_w)$, the algebra of all bounded linear operators on…
In this article we obtain an explicit formula for certain Rankin-Selberg type Dirichlet series associated to certain Siegel cusp forms of half-integral weight. Here these Siegel cusp forms of half-integral weight are obtained from the…
``In this paper we give the history of Leonhard Euler's work on the pentagonal number theorem, and his applications of the pentagonal number theorem to the divisor function, partition function and divergent series. We have attempted to give…
Euler gives a long introduction, giving all the arguments for and against the use of divergent series in calculus and then gives his own definition of the sum of a diverging series. Then in the second half of this paper he evaluates the the…
This paper presents the construction of the Seiberg-Witten-Floer homology of three-manifolds with non-trivial rational homology, and some properties of the invariant of three-manifolds obtained by computing the Euler characteristic. This…
The title says what is done here. Euler finds a news series for the arc of an ellipse. The paper is translated from the Latin original into German.
The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968
Rejoinder: Expert Elicitation for Reliable System Design [arXiv:0708.0279]
The thesis concerns Hilbert schemes of points and apart from mathematical results, contains small open problems and history sections, see the introduction for more details. The thesis has not been edited since 2017, see first page for more…
The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.
Some statements concerning the distribution of imaginary parts of zeros of the Riemann zeta\,-function are established. These assertions are connected with so\,-called `Gram's law' or `Gram's rule'. In particular, we give a proof of several…
The paper extends some well-known results for analytic functions onto solutions of the Vekua equation $\partial _{\overline{z}}W=aW+b\overline{W}$ regarding the existence and construction of the Bergman kernel and of the corresponding…
This article represents a personal tribute to Richard Askey together with a new look at some of his favorite integrals, including the Cauchy beta integral. The article also provides some new multidimensional extensions of Cauchy's beta…
We connect Dedekind sums and some formulas for numerical semigroups.
This paper contains all computations supporting the classification of 7-dimensional Einstein nilradicals given in the article "Classification of 7-dimensional Einstein nilradicals" (arXiv). Each algebra is analyzed in detail here.
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
A treatment of (generalized) Clemens-Schmid exact sequences from the perspective of weights.
The present report, has been inspired by the need of the author and its colleagues to understand the underlying theory of Wirtinger's Calculus and to further extend it to include the kernel case. The aim of the present manuscript is…