Related papers: Effective decorrelation of Hecke eigenforms

We establish the two-dimensional asymptotic distributions of the logarithm and logarithmic derivative of $L$-functions associated with a family of cubic Hecke characters. A crucial ingredient in the proof of our main result is an…

Using the language of coarse homology theories, we provide an axiomatic account of vanishing results for the fibres of forget-control maps associated to spaces with equivariant finite decomposition complexity.

In this paper we study the center algebras of multilinear forms. It is shown that the center of a nondegenerate multilinear form is a finite dimensional commutative algebra and can be effectively applied to its direct sum decompositions. As…

Let $q:=e^{2 \pi iz}$, where $z \in \mathbb{H}$. For an even integer $k$, let $f(z):=q^h\prod_{m=1}^{\infty}(1-q^m)^{c(m)}$ be a meromorphic modular form of weight $k$ on $\Gamma_0(N)$. For a positive integer $m$, let $T_m$ be the $m$th…

We shall present an elementary approach to extremal decompositions of (quantum) covariance matrices determined by densities. We give a new proof on former results and provide a sharp estimate of the ranks of the densities that appear in the…

Given a self-dual cuspidal automorphic representation for GL(2) over a number field, we establish the existence of an infinite number of Hecke eigenvalues that are greater than an explicit positive constant, and an infinite number of Hecke…

We sharpen some estimates of Rankin on power sums of Hecke eigenvalues, by using Kim & Shahidi's recent results on higher order symmetric powers. As an application, we improve Kohnen, Lau & Shparlinski's lower bound for the number of Hecke…

The mass correction forms of the arbitrary spin heavy hadrons are derived by using the projection operator method. The Bjorken sum rule for finite mass is derived by using the results of here.

In this notes we describe the center and derivations of the Infinitesimal Hecke algebra of $sl_2$ by means of elementary computations.

We prove that Hecke eigenvalues for any Hilbert and Siegel modular forms are algebraic integers. Our method does not rely on cohomologicality nor Galois representations. We apply the integrality of Hecke eigenvalues for Hilbert modular…

We prove effective Nullstellensatz and elimination theorems for difference equations in sequence rings. More precisely, we compute an explicit function of geometric quantities associated to a system of difference equations (and these…

A short review of a few selected topics in Heavy Quark Effective Theory is given. Applications to exclusive decays are discussed.

The QED effective action at finite temperature and density is calculated to all orders in an external homogeneous and time-independent magnetic field in the weak coupling limit. The free energy, obtained explicitly, exhibit the expected de\…

Given a conformal metric with finite total Q-curvature, we show that the assumptions on scalar curvature sensitively govern the Q-curvature integral. Additionally, we introduce a conformal mass for such manifolds. Using such mass, we…

Let L be an ample holomorphic line bundle over a compact complex Hermitian manifold X. Any fixed smooth Hermitian metric on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k:th tensor power…

We prove an Erd\H{o}s--Tur\'an type inequality for compact Lie groups, from which we deduce an effective version of Deligne's equidistribution theorem.

We summarize first results for masses and decay constants of bottom-strange (pseudo-scalar and vector) mesons from nonperturbatively renormalized heavy-quark effective theory (HQET), using lattice-QCD simulations in the quenched…

Consider a complex line bundle over a compact complex manifold equipped with an infinitely differentiable metric with strictly positive curvature form. Assign to positive tensor powers of this bundle the associated product metrics and…

We study the unitary boundary representation of a strongly transitive group acting on a right-angled hyperbolic building. We show its irreducibility. We do so by associating to such a representation a representation of a certain Hecke…

This paper is concerned with superconvergence properties of a class of finite volume methods of arbitrary order over rectangular meshes. Our main result is to prove {\it 2k-conjecture}: at each vertex of the underlying rectangular mesh, the…