Related papers: A note on a classical relative trace formula

This paper is a continuation of previous work of the author. We use the categorical trace formalism to give a construction of the categorical Jordan decomposition for representations of finite groups of Lie type. As a second application, we…

The goal of this paper is to construct trace maps for the six functor formalism of motivic cohomology after Voevodsky, Ayoub, and Cisinski-D\'{e}glise. We also construct an $\infty$-enhancement of such a trace formalism. In the course of…

We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions and clarify the theoretical connection between the Trace…

Let $A$ be a selfadjoint operator in a separable Hilbert space, $K$ a selfadjoint Hilbert-Schmidt operator, and $f\in C^n(\mathbb{R})$. We establish that $\varphi(t)=f(A+tK)-f(A)$ is $n$-times continuously differentiable on $\mathbb{R}$ in…

A recent proposal relates two dimensional holographic conformal field theories deformed by the integrable $T\bar{T}$ flow to AdS$_3$ with a finite radial cutoff. We investigate this proposal by studying perturbative correlation functions on…

In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…

New formulas for approximation of zeta-constants were derived on the basis of a number-theoretic approach constructed for the irrationality proof of certain classical constants. Using these formulas it's possible to approximate certain…

Let $G$ be a connected quasi-split reductive group over $\mathbb{R}$, and more generally, a quasi-split $K$-group over $\mathbb{R}$. Arthur had obtained the formal formula for the spectral side of the stable local trace formula, by using…

This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this…

We reprove a Waldspurger's formula which relates the toric periods and the central values of L-functions of GL2. Our technique, different from the original theta-correspondence approach and the more recent relative trace formula, relies on…

In this paper, we obtain some new estimates for the trace and inverse trace of Steklov eigenvalues. The estimates generalize some previous results of Hersch-Payne-Schiffer , Brock}, Raulot-Savo and Dittmar.

We define a unified trace form $\tau$ on the cyclotomic Hecke algebras $\mathscr{H}_{n,K}$ of type $A$, which generalize both Malle-Mathas' trace form on the non-degenerate version (with Hecke parameter $\xi\neq 1$) and Brundan-Kleshchev's…

Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, for the Lefschetz number of D as the…

We assemble three basic analytic inputs -- the Kuznetsov trace formula on $\mathrm{SL}_2(\mathbb Z)$ with explicit continuous spectrum, the $\mathrm{GL}_3$ Voronoi formula, and $t$-aspect second-moment bounds for $L(1/2+it,\varphi)$ -- into…

Our goal is to establish a hidden regularity result for solutions of time fractional Petrovsky system where the Caputo fractional derivative is of order $\alpha\in(1,2)$. We achieve such result for a suitable class of weak solutions.

We study an invariant, the secondary trace, attached to two commuting endomorphisms of a 2-dualizable object in a symmetric monoidal higher category. We establish a secondary trace formula which encodes the natural symmetries of this…

In this work derivations of definite integrals listed in Prudnikov volume I, Gradshteyn and Ryzhik and a few other tables are produced. Special cases of these integrals in terms of fundamental constants are also evaluated. The method used…

We obtain the formula for the twisted harmonic second moment of the $L$-functions associated with primitive Hecke eigenforms of weight 2. A consequence of our mean value theorem is reminiscent of recent results of Conrey and Young on the…

Based on the notion of the resolvent and on the Hilbert identities, this paper presents a number of classical results in the theory of differential operators and some of their applications to the theory of automorphic functions and number…

Let f: X -> Z be a separated essentially-finite-type flat map of noetherian schemes, and \delta: X --> X \times_Z X the diagonal map. The fundamental class C_f (globalizing residues) is a map from the relative Hochschild functor…