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Fuchsian systems for Dotsenko-Fateev multipoint correlation functions and similar integrals of hypergeometric type
Journal of Geometry and Physics. 2017. Vol. 116. P. 216–227.
Golubeva V. A., Ivanov A. N.
The Dotsenko-Fateev integral is an analytical function of one complex variable expressing the amplitude in the 4-point correlator of the 2D conformal field theory. Dotsenko-Fateev found ODE of third order with Fuchsian singularities satisfied by their integral. In the present paper, this work is extended to generalized Dotsenko-Fateev integrals, in particular those associated to arbitrary multipoint correlators, and Pfaff systems of PDE of Fuchsian type are constructed for them. The ubiquity of the Fuchsian systems is in that they permit to obtain local expansions of solutions in the neighborhoods of singularities of the system.
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...
Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Belousov N. M., Sarkissian G. A., Spiridonov V. P., Analysis and Mathematical Physics 2026 Vol. 16 Article 96
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...
Added: August 4, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Spiridonov V., Sarkissian G. A., / Series arXiv "math". 2021. No. arXiv:2105.15031.
General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. Derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable N-body systems emerging from particular degenerations of the elliptic Ruijsenaars and van Diejen models. ...
Added: November 9, 2021
Springer, 2020.
This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2019 International Symposium, which was held at the University of Szeged, Bolyai Institute and the Hungarian Academy of Sciences, Hungary, October 21st-25th, 2019. The topics covered in this volume include tumor and infection modeling; dynamics of co-infections; epidemic models on networks; ...
Added: March 11, 2021
Gravin N., Pasechnik D., Shapiro B. et al., Analysis and Mathematical Physics 2018 Vol. 8 No. 2 P. 255–287
We show that the multivariate generating function of appropriately normalized moments of a measure with homogeneous polynomial density supported on a compact polytope P subset of R-d is a rational function. Its denominator is the product of linear forms dual to the vertices of P raised to the power equal to the degree of the ...
Added: February 25, 2021
Vasily M. Goncharenko, Alexander B. Shapoval, Lipagina L., , in: Proceedings of the Conference on Modeling and Analysis of Complex Systems and Processes 2020 (MACSPro 2020)Vol. 2795.: CEUR Workshop Proceedings, 2020. P. 108–116.
We consider a general equilibrium model in a multisector economy with 𝑛 high-tech sectors where singleproduct firms compete monopolistically producing a differentiated good. Homogeneous sector is characterized by perfect competition. Workers attempt to find a job in high-tech sectors because of higher wages. However, it is possible for them to remain unemployed. Wages of employees ...
Added: January 13, 2021
Frolenkov D., Journal of Number Theory 2020 Vol. 207 No. 2 P. 247–281
We prove an explicit formula for the cubic moment of central values of automorphic
$L$-functions associated to primitive cusp forms of level one and large weight.
The resulting explicit formula contains the main term predicted by the random matrix theory conjectures, while the error term is expressed as the fourth moment of the Riemann zeta function weighted ...
Added: September 25, 2020
Balkanova O., Bhowmik G., Frolenkov D. et al., Proceedings of the London Mathematical Society 2020 Vol. 121 No. 2 P. 177–219
Let $ \mathfrak{f} $ run over the set $ H_{4k} $ of primitive cusp forms of level one and weight $ 4k $, $ k \in \N $.
We prove an explicit formula for the mixed moment of the Hecke $L$-function $ L(\mathfrak{f}, 1/2) $ and the symmetric square $L$-function $L(\sym^2\mathfrak{f}, 1/2)$, relating it to the ...
Added: September 25, 2020
Esterov A. I., Takeuchi K., Nagoya Mathematical Journal 2018 Vol. 231 P. 1–22
We prove some vanishing theorems for the cohomology groups of local systems associated to Laurent polynomials. In particular, we extend one of the results of Gelfand et al. [Generalized Euler integrals and A-hypergeometric functions, Adv. Math. 84 (1990), 255–271] to various directions. In the course of the proof, some properties of vanishing cycles of perverse sheaves ...
Added: October 31, 2018