This paper investigates the structure of twisted Jacquet modules of certain representations of GL2(D), where D is a division algebra over a non-archimedean local field, proving a conjecture by D. Prasad in the case of the quaternionic division algebra and providing dimension formulas and explicit descriptions in the depth-zero case.
This paper establishes branching rules for finite-dimensional unitary simple modules of the general linear Lie superalgebra (glm|n), providing necessary and sufficient conditions for their decomposition into simple unitary glm|n-1-modules.
The Koebe circle domain conjecture, which posits that any planar domain is conformally equivalent to a circle domain, is equivalent to a specific formulation of the Weyl problem in hyperbolic 3-space, asserting that every complete hyperbolic surface of genus zero is isometric to the boundary of the hyperbolic convex hull of a circle type closed set in the sphere at infinity.
This paper introduces the concept of (∞, 2)-topoi, a higher-categorical generalization of topoi, characterized by a "fibrational descent" axiom, and explores its implications for developing a synthetic theory of (∞, 1)-categories.
The moments of the cot function can be expressed in terms of recursive sums and integrals as a linear combination of the Dirichlet eta functions at odd integers, using a new integral representation of the central factorial numbers.
This paper derives various identities and multiple angle formulas for degenerate trigonometric functions, including degenerate sine, cosine, tangent, and cotangent functions.
This work establishes systems of partial differential equations satisfied by 205 complete and 395 confluent hypergeometric functions of three variables, and determines particular solutions of the constructed systems near the origin, if such solutions exist.
The article presents a solution to the truncated two-dimensional moment problem using the Schur algorithm, which is based on the continued fraction expansion of the solution. The results are applicable to the two-dimensional moment problem for atomic measures.
This paper presents a geometric method for finding the roots of a quadratic equation in one complex variable by constructing a line and a circumference in the complex plane, using the known coefficients of the equation.
Large language models (LLMs) demonstrate significant capabilities in solving math problems, but they tend to produce hallucinations when given questions containing unreasonable errors.