相关论文: A general simple relative trace formula and a rela…
We give a short proof of the trace formula for Hecke operators on modular forms for the modular group, using the action of Hecke operators on the space of period polynomials.
We provide a gauge-invariant theory of gravitation in the context of Weyl Integrable Space-Times. After making a brief review of the theory's postulates, we carefully define the observers' proper-time and point out its relation with…
We give a trace inequality related to the uncertainty relation based on the monotone or anti-monotone pair skew information which is one of generalizations of result given by Ko and Yoo. It includes our result for generalized…
We introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while preserving much of its geometric implications.…
We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature…
For the group G=PGL_2 we perform a comparison between two relative trace formulas: on one hand, the relative trace formula of Jacquet for the quotient T\backslash G/T, where T is a non-trivial torus, and on the other the Kuznetsov trace…
We prove an analogue of Weyl's law for quantized irreducible generalized flag manifolds. By this we mean defining a zeta function, similarly to the classical setting, and showing that it satisfies the following two properties: as a…
Following a scheme inspired by B. Feigon, we describe the spectral side of a local relative trace formula for $G:= PGL(2,\rm E)$ relative to the symmetric subgroup $H:=PGL(2,\rm F)$ where $\rm E/\rm F$ is an unramified quadratic extension…
We survey several generalizations of the Weyl algebra including generalized Weyl algebras, twisted generalized Weyl algebras, quantized Weyl algebras, and Bell-Rogalski algebras. Attention is paid to ring-theoretic properties,…
In this paper, we prove an exponential integral formula for the Fourier transform of Bessel functions over complex numbers, along with a radial exponential integral formula. The former will enable us to develop the complex spectral theory…
In this short paper, we give a complete and affirmative answer to a conjecture on matrix trace inequalities for the sum of positive semidefinite matrices. We also apply the obtained inequality to derive a kind of generalized Golden-Thompson…
We introduce a new family of twisted generalized Weyl algebras, called multiparameter twisted Weyl algebras, for which we parametrize all simple quotients of a certain kind. Both Jordan's simple localization of the multiparameter quantized…
The purpose of this short article is to prove a product formula relating the log Gromov-Witten invariants of $V \times W$ with those of $V$ and $W$ in the case the log structure on $V$ is trivial.
We introduce a generalization of relative entropy derived from the Wigner-Yanase-Dyson entropy and give a simple, self-contained proof that it is convex. Moreover, special cases yield the joint convexity of relative entropy, and for the map…
The goal of this paper is to generalize a theorem of Fujiwara (formerly Deligne's conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our…
In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.
The Weyl double copy is a relationship between classical solutions in gauge and gravity theories, and has previously been applied to vacuum solutions in both General Relativity and its generalisations. There have also been suggestions that…
In this note we provide a simple formula of general term of recurrent sequence.
We classify up to isomorphism the quantum generalized Weyl algebras and determine their automorphism groups in all cases in a uniform way, including those where the parameter q is a root of unity, thereby completing the results obtained by…
We consider the Principle of Equivalence along with Weyl theorem to discuss the interpretation of gravity as a geometric effect; we study what are the restrictions on the connections that must be required for this geometrization to occur in…