Related papers: Sur le spectre des longueurs des groupes de triang…

We obtain an upper bound for the multiplicative energy of the spectrum of an arbitrary set from $\mathbb{F}_p$, which is the best possible up to the results on exponential sums over subgroups.

In this survey we discuss some combinatorial aspects of higher cluster categories.

We present results related to determination of the Unitarity Triangle angle phi_3.

We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…

This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.

In this paper, we consider the distance spectra of the derangement graphs. First we give a constructive proof that the connected derangement graphs are of diameter 2. Then we obtain their distance spectra. In particular, we determine all…

In this article, we establish polynomial-growth bound for the sequence of Fourier coefficients associated to even integer weight vector-valued automorphic forms of Fuchsian groups of the first kind. At the end, their $L$-functions and…

In this paper, the concept of a picture fuzzy subgroup of a group is studied, and the notion of the direct product of picture fuzzy subgroups is introduced. Several characterisations of the direct product of picture fuzzy subgroups are…

We present a method for computing upper bounds on the systolic length of certain Riemann surfaces uniformized by congruence subgroups of hyperbolic triangle groups, admitting congruence Hurwitz curves as a special case. The uniformizing…

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

Some questions of application of trigonometric splines in problems of spectral analysis are considered. The known effects of overlay in the frequency and time domains are discussed; deployment effects in these areas are firstly considered.…

This is a survey on spectral theory of dynamical systems.

These are lecture notes on string theory at Fudan University.

In this talk, some aspects of duality symmetries are presented.

An overview of some basic notions is given, especially with an eye towards somewhat "fractal" examples, such as infinite products of cyclic groups, p-adic numbers, and solenoids.

We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in…

In connection to the Fuglede conjecture, and to Fuglede's original work \cite{Fug74}, we study one-parameter unitary groups associated to self-adjoint extensions of the differential operator $Df=\frac1{2\pi i}f'$ on a union of finite…

In this short note we answer some questions of Bergman regarding homomorphic images of (ultra)products of groups.

We obtain upper bounds on the composition length of a finite permutation group in terms of the degree and the number of orbits, and analogous bounds for primitive, quasiprimitive and semiprimitive groups. Similarly, we obtain upper bounds…

In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…