Related papers: Nearest lambda_q-multiple fractions

This is about Curtis conjecture on the image of the Hurewicz map $h:{_2\pi_*}Q_0S^0\to H_*(Q_0S^0;\Z/2)$. First, we show that if $f\in{_2\pi_*^s}$ is of Adams filtration at least $3$ with $h(f)\neq 0$ then $f$ is not a decomposable element…

An $L(h_1, h_2, \ldots, h_l)$-labelling of a graph $G$ is a mapping $\phi: V(G) \rightarrow \{0, 1, 2, \ldots\}$ such that for $1\le i\le l$ and each pair of vertices $u, v$ of $G$ at distance $i$, we have $|\phi(u) - \phi(v)| \geq h_i$.…

The problem of investigation of the simplest n-dimensional continued fraction in the sense of Klein for n>2 was posed by V.Arnold. The answer for the case of n=2 can be found in the works of E.Korkina and G.Lachaud. In present work we study…

Our aim is to find a complex continued fraction algorithm finding all the best Diophantine approximations to a complex number. Using the sequence of minimal vectors in a two dimensional lattice over Gaussian integers, we obtain an algorithm…

The first known $q$-analogues for any of the $17$ formulas for $\frac{1}{\pi}$ due to Ramanujan were introduced in 2018 by Guo and Liu (J. Difference Equ. Appl. 29:505-513, 2018), via the $q$-Wilf-Zeilberger method. Through a…

In this paper we establish the $L^p$-$L^q$ boundedness of Fourier multipliers on locally compact separable unimodular groups for the range of indices $1<p\leq 2 \leq q<\infty$. Our approach is based on the operator algebras techniques. The…

We study the generalized continued fraction expansions of complex numbers in term of elements from Euclidean subrings, especially Gaussian or Eisenstein integers, in a general framework as pursued in [3] and [1]. We introduce a common…

This article deals with the tamely ramified geometric Langlands correspondence for GL_2 on $\mathbf{P}_{\mathbf{F}_q}^1$, where $q$ is a prime power, with tame ramification at four distinct points $D = \{\infty, 0,1, t\} \subset…

Hecke algebras are usually defined algebraically, via generators and relations. We give a new algebro-geometric construction of affine and double-affine Hecke algebras (the former is known as the Iwahori-Hecke algebra, and the latter was…

We study the topological, dynamical, and descriptive set theoretic properties of Hurwitz continued fractions. Hurwitz continued fractions associate an infinite sequence of Gaussian integers to every complex number which is not a Gaussian…

We show that the Gutzwiller variational wave function is surprisingly accurate for the computation of magnetic phase boundaries in the infinite dimensional Hubbard model. This allows us to substantially extend known phase diagrams. For both…

In this paper we introduce two new fractional versions of the Laplacian. The first one is based on the classical formula that writes the usual Laplacian as the sum of the eigenvalues of the Hessian. The second one comes from looking at the…

We are extending results from \cite{B-Hurwitz} by building a parallel theory of simple Hurwitz numbers for the reflection groups $G(m,1,n)$. We also study analogs of the cut-and-join operators. An algebraic description as well as a…

The $q$-Whittaker function $W_\lambda(\mathbf{x};q)$ associated to a partition $\lambda$ is a $q$-analogue of the Schur function $s_\lambda(\mathbf{x})$, and is defined as the $t=0$ specialization of the Macdonald polynomial…

Let $\boldsymbol{\alpha}\in \mathbb{R}^N$ and $Q\geq 1$. We consider the sum $\sum_{\boldsymbol{q}\in [-Q,Q]^N\cap\mathbb{Z}^N\backslash\{\boldsymbol{0}\}}\|\boldsymbol{\alpha}\cdot\boldsymbol{q}\|^{-1}$. Sharp upper bounds are known when…

Let $T_n$ be the linear Hadamard convolution operator acting over Hardy space $H^q$, $1\le q\le\infty$. We call $T_n$ a best approximation-preserving operator (BAP operator) if $T_n(e_n)=e_n$, where $e_n(z):=z^n,$ and if $\|T_n(f)\|_q\le…

We describe a graded extension of the usual Hecke algebra: it acts in a graded fashion on the cohomology of an arithmetic group $\Gamma$. Under favorable conditions, the cohomology is freely generated in a single degree over this graded…

In this paper we study a geometric coding algorithm for indefinite binary quadratic forms Q for the congruence subgroup \Gamma^0(N), with respect to the usual fundamental domain FN, where N is assumed prime. The cycles Q_1, . . ., Q_n that…

We prove the analogue of Malle's conjecture for the global function field $\F_q(t)$ with $q$ sufficiently large, including a precise formula for the leading constant. The main ingredients are the recent breakthrough of Landesman--Levy on…

Based on the fractional $q$-integral with the parametric lower limit of integration, we define fractional $q$-derivative of Riemann-Liouville and Caputo type. The properties are studied separately as well as relations between them. Also, we…