Related papers: Rankin Triple Products and Quantum Chaos
We establish results on the rationality of ratios of successive critical values of Langlands-Shahidi $L$-functions, as they appear in the constant term of the Eisenstein series associated with the exceptional group of type $G_2$ over a…
We compute the stable homology of the braid group with coefficients in any Schur functor applied to the integral reduced Burau representation. This may be considered as a hyperelliptic analogue of the Mumford conjecture (Madsen--Weiss…
Let $\pi$ be a cuspidal automorphic representation of $\operatorname{GL}_2$ over a totally real number field $F$. Let $K$ be a totally imaginary quadratic extension of $F$. We estimate central values of the $\operatorname{GL}_2 \times…
We show that recent improvements in the $O(\alpha)$ long-distance quantum electrodynamics (QED) corrections to the radiative inclusive $K_{e3}$ decay rate using the Sirlin representation are free from infrared divergences and collinear…
The Karman-Howarth-Monin-Hill (KHMH) equation has been widely applied to scale-by-scale turbulent energy cascade studies in recent years, however, the forms and interpretations are not consistent. The present work generalizes to considering…
We p-adically interpolate the relative de Rham cohomology of the universal elliptic curve over strict neighbourhoods of the ordinary locus of modular curves, together with the Hodge filtration and Gauss-Manin connection. Sections of these…
For $\Gamma$ a cofinite Kleinian group acting on $\mathbb{H}^3$, we study the Prime Geodesic Theorem on $M=\Gamma \backslash \mathbb{H}^3$, which asks about the asymptotic behaviour of lengths of primitive closed geodesics (prime geodesics)…
We quantize a compactified version of the trigonometric Ruijse\-naars-Schneider particle model with a phase space that is symplectomorphic to the complex projective space CP^N. The quantum Hamiltonian is realized as a discrete difference…
This is a survey of recent results on quantum ergodicity, specifically on the large energy limits of matrix elements relative to eigenfunctions of the Laplacian. It is mainly devoted to QUE (quantum unique ergodicity) results, i.e. results…
We develop a hybrid Euler-Hadamard product model for quadratic Dirichlet $L$--functions over function fields (following the model introduced by Gonek, Hughes and Keating for the Riemann-zeta function). After computing the first three…
We prove that there are infinitely many Maass--Hecke cuspforms over the field $\mathbb{Q}[\sqrt{-3}]$ such that the corresponding symmetric cube $L$-series does not vanish at the center of the critical strip. This is done by using a result…
We provide Harish-Chandra type formulas for the multivariate Bessel functions and Heckman-Opdam hypergeometric functions as representation-valued integrals over dressing orbits. Our expression is the quasi-classical limit of the realization…
We prove a quantitative finiteness theorem for the number of totally geodesic hyperplanes of non-arithmetic hyperbolic $n$-manifolds that arise from a gluing construction of Gromov and Piatetski-Shapiro for $n\ge3$. This extends work of…
We prove Deligne's conjecture for central critical values of certain automorphic $L$-functions for ${\rm GL}(3)\times {\rm GL}(2)$. The proof is base on rationality results for central critical values of triple product $L$-functions, which…
In this note, we prove in full generality a conjecture of Jacquet concerning the nonvanishing of the triple product L-function at the central point. Let $\kay$ be a number field and let $\pi_i$, $i=1$, 2, 3 be cuspidal automorphic…
We prove strong hybrid subconvex bounds simultaneously in the $q$ and $t$ aspects for $L$-functions of selfdual $\mathrm{GL}_3$ cusp forms twisted by primitive Dirichlet characters. We additionally prove analogous hybrid subconvex bounds…
We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds of arithmetic type. The manifolds under consideration are d-fold products of 2-spheres or 3-spheres, realized as adelic quotients of quaternion algebras…
The Lichtenbaum-Quillen conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define the "Lichtenbaum-Quillen dimension" of a variety in terms…
In this paper we present explicit formulas for the *-product on quantum spaces which are of particular importance in physics, i.e., the q-deformed Minkowski space and the q-deformed Euclidean space in 3 and 4 dimensions, respectively. Our…
In this work we find that not only the Heisenberg-like uncertainty products and the R\'enyi-entropy-based uncertainty sum have the same first-order values for all the quantum states of the $D$-dimensional hydrogenic and oscillator-like…