Related papers: A formula for Gau{\ss}-Manin determinants

Quadratic fluctuations require an evaluation of ratios of functional determinants of second-order differential operators. We relate these ratios to the Green functions of the operators for Dirichlet, periodic and antiperiodic boundary…

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The determinant of the Gaussian unitary ensemble matrix is show to be distributed as a product of independent chi random variables with parameters $1,3,3,5,5,\dots.$

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We use the Jacobi-Trudi formula to execute "explicit" evaluation of determinants of Stirling numbers of both kinds. We also offer a Maple package accompanying the paper on the personal websites at the end of the second page.

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Welschinger invariants of the real projective plane can be computed via the enumeration of enriched graphs, called marked floor diagrams. By a purely combinatorial study of these objects, we prove a Caporaso-Harris type formula which allows…

The fundamental matrix solution of the quantum Knizhnik-Zamolodchikov equation associated with quantum affine sl2 algebra is constructed for |q|=1. The formula for its determinant is given in terms of the double sine function.

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We characterise the class of probability operators belonging to the domain of attraction of Gaussian limits in the setup which is a slight generalisation of Urbanik's scheme of noncommutative probability limit theorems.

Let $G$ be a finite $p$-group. We construct a $G$-extension $K/k$ of number fields such that the $p$-adic completion of the unit group of $K$ has a prescribed $\mathbb{Z}_p[G]$-module structure, up to free direct summands.

Pour tout sch\'ema simplicial complexe $X_{\bullet}$ il existe une application canonique $\nabla:H^{\ast}(X_{\bullet})\longrightarrow \Omega^1_{{\mathbb C}/{\mathbb Q}}\otimes H^{\ast}(X_{\bullet})$, appel\'ee la connexion de Gau\ss-Manin.…