相关论文: A formula for Gau{\ss}-Manin determinants

We consider a family $\{T_N:N \geq 1 \}$ of interval maps as generalizations of the Gauss transformation. For the continued fraction expansion arising from $T_N$, we solve its Gauss-Kuzmin-type problem by applying the theory of random…

Gaussian graphical models are parametric statistical models for jointly normal random variables whose dependence structure is determined by a graph. In previous work, we introduced trek separation, which gives a necessary and sufficient…

We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…

We resolve an ambiguity in the sign of the gaugino determinant in supersymmetric models. The result, that the gaugino determinant can be taken positive for all background gauge configurations, is necessary for application of QCD…

We present a novel approach to Gaussian Berezin correlation functions. A formula well known in the literature expresses these quantities in terms of submatrices of the inverse matrix appearing in the Gaussian action. By using a recently…

We establish a correspondence between the disk invariants of the complex projective line $\bP^1$ with boundary condition specified by an $S^1$-invariant Lagrangian sub-manifold $L$ and the genus-zero closed Gromov-Witten invariants of a…

We prove a determinant formula for the standard integral form of a lattice vertex operator algebra.

When $E$ is an $R$-module over a commutative unital ring $R$, the Zariski closure of its support is of the form $\mathrm V(\mathcal O(E))$ where $\mathcal O(E)$ is a unique radical ideal. We give an explicit form of $\mathcal O(E)$ and…

One studies the system of differential equations satisfied by the hyperelliptic integral associated to a vanishing cycle defined for the versal deformation of the $A-\mu$ singularity. As an application, the estimates on the multiplicity of…

We investigate, analytically and numerically, the fermion determinant of a new action on a (1+1)-dimensional Euclidean lattice. In this formulation the discrete chiral symmetry is preserved and the number of fermion components is a half of…

We define a determinant on the Toeplitz algebra associated to a minimal flow, give a formula for this determinant in terms of symbols, and show that this determinant can be used to give information about the algebraic $K$-theory of…

Pausinger recently investigated a special determinant involving prime numbers. In this short note we point out that this type of determinants was already known in linear algebra and its computation is unrelated to prime numbers.

In this paper we treat a non-Gaussian integral and give a fundamental formula in terms of discriminant. We also present some related problems. This is a comment paper to arXiv:0903.2595 [math-ph] by Morozov and Shakirov.

A system of differential equations of the Okubo normal form containing accessory parameters is considered. A condition for determining special values of the accessory parameters is given. It is shown that the special values give the…

We study the geometry of determinant line bundles associated to Dirac operators on compact odd dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the…

In this paper, we investigate the determinants involving some trigonometric functions. We establish a connection between these determinants and the special values of Dirichlet L-functions, thereby extending Guo's results to arbitrary…

In a previous paper [KT] we introduced determinant of the Riemann operator on Quillen's higher $K$-groups of the integer ring of an algebraic number field $K$. We showed that the determinant expresses essentially the inverse of the so…

The difference Galois theory of Mahler equations is an active research area. The present paper aims at developing the analytic aspects of this theory. We first attach a pair of connection matrices to any regular singular Mahler equation. We…

We present a discrete formulation of the Kane-Mele $\mathbb{Z}_2$ invariant that is manifestly gauge-independent and quantized.

A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…