Related papers: Rankin Triple Products and Quantum Chaos

We show that tensor products of $k$ gradients of harmonic functions, with $k$ at least three, are dense in $C(\overline{\Omega})$, for any bounded domain $\Omega$ in dimension 3 or higher. The bulk of the argument consists in showing that…

We classify Nichols algebras of irreducible Yetter-Drinfeld modules over groups such that the underlying rack is braided and the homogeneous component of degree three of the Nichols algebra satisfies a given inequality. This assumption…

We prove that for any free ergodic nonsingular nonamenable action \Gamma\ \actson (X,\mu) of all \Gamma\ in a large class of groups including all hyperbolic groups, the associated group measure space factor $L^\infty(X) \rtimes \Gamma$ has…

We obtain exact formulas for central values of triple product L-functions averaged over newforms of weight 2 and prime level. We apply these formulas to non-vanishing problems. This paper uses a period formula for the triple product…

We establish the first moment bound $$ \sum_{\varphi} L(\varphi \otimes \varphi \otimes \Psi, \tfrac{1}{2}) \ll_{\varepsilon} p^{5/4+\varepsilon} $$ for triple product $L$-functions, where $\Psi$ is a fixed Hecke-Maass form on…

We prove a variety results on tensor product factorizations of finite dimensional Hopf algebras (more generally Hopf algebras satisfying chain conditions in suitable braided categories). The results are analogs of well-known results on…

Hamiltonian tridiagonal matrices characterized by multi-fractal spectral measures in the family of Iterated Function Systems can be constructed by a recursive technique here described. We prove that these Hamiltonians are almost-periodic.…

Consider three normalised cuspidal eigenforms of weight $2$ and prime level $p$. Under the assumption that the global root number of the associated triple product $L$-function is $+1$, we prove that the complex Abel-Jacobi image of the…

We give a soft proof of a uniform upper bound for the local factors in the triple product formula, sufficient for deducing effective and general forms of quantum unique ergodicity (QUE) from subconvexity.

We consider the three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the Earth's fluid core. We examine the multi-parameter singular…

We prove that the quotients of the group algebra of the braid group on 3 strands by a generic quartic and quintic relation respectively, have finite rank. This is a special case of a conjecture by Brou\'{e}, Malle and Rouquier for the…

Given a representation of a link group, we introduce a trilinear form, as a topological invariant. We show that, if the link is either hyperbolic or a knot with malnormality, then the trilinear form equals the pairing of the (twisted)…

For any triple $(W,L,\rho)$, where W is a closed connected and oriented 3-manifold, L is a link in W and $\rho$ is a flat principal B-bundle over W (B is the Borel subgroup of $SL(2,\mc)$), one constructs a $\Dd$-scissors congruence class…

Using a model Hamiltonian for a single-mode electromagnetic field interacting with a nonlinear medium, we show that quantum expectation values of subsystem observables can exhibit remarkably diverse ergodic properties even when the dynamics…

Quantum deformed potentials arise naturally in quantum mechanical systems of one bosonic coordinate coupled to $N_f$ Grassmann valued fermionic coordinates, or to a topological Wess-Zumino term. These systems decompose into sectors with a…

We study the limiting behavior of Maass forms on Benjamini-Schramm convergent sequences of compact quotients of ${\rm SL}_d(\mathbb{R})/{\rm SO}(d)$, $d\ge 3$, whose spectral parameter stays in a fixed window. We prove a form of Quantum…

We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a…

In this paper, we focus on the strong subconvexity bounds for triple product L-functions in the cubic level aspect. Our proof on the Weyl-type bound synthesizes techniques from classical analytic number theory with methods in automorphic…

Let $\pi : X \to B$ be an elliptically fibered threefold satisfying $c_3(T_X \otimes \omega_X)=0$. We conjecture that the $\pi$-relative generating series of Pandharipande-Thomas invariants of $X$ are quasi-Jacobi forms and satisfy two…

We give parallel constructions of an invariant R(W,f), based on the classical Rogers dilogarithm, and of quantum hyperbolic invariants (QHI), based on the Faddeev-Kashaev quantum dilogarithms, for flat PSL(2,C)-bundles f over closed…