Related papers: Multiplicity One Theorems, S-Version

We obtain upper bounds on the number of finite sets $\mathcal S$ of primes below a given bound for which various $2$ variable $\mathcal S$-unit equations have a solution.

We extend the theory (formal part only} of algebras with one binary operation (our paper arXiv:math/0110333v1 [math.RA] 31 Oct 2001) to algebras with several operations of any arity.

We prove an analogue of the strong multiplicity one theorem in the context of $\tau_n$-spherical representations of the group $G = SO(2,1)^\circ$ appearing in $L^2(\Gamma_i \backslash G)$ for uniform torsion-free lattices $\Gamma_i, i = 1,…

We present a new, elementary, dynamical proof of the prime number theorem.

An approximation result for the bilinear Hilbert transform is proved and used for the inversion of the bilinear Hilbert transform. Also, p-Lebesgue points $(p\geq 1)$ are analyzed.

We give a new proof of Lucas' Theorem in elementary number theory.

We construct a family of representations of an arbitrary variant $S_a$ of a semigroup $S$, induced by a given representation of $S$, and investigate properties of such representations and their kernels.

We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.

It was asked by Marques-Neves which min-max $p$-widths of the unit $3$-sphere lie strictly between $2\pi^2$ and $8\pi$. We show that the 10th to the 13th widths do. More generally, we prove stronger versions of X. Zhou's multiplicity one…

We prove a new cross theorem for separately holomorphic functions.

For a wide class of integer linear recurrence sequences $\left(u(n)\right)_{n=1}^\infty$, we give an upper bound on the number of $s$-tuples $\left(n_1, \ldots, n_s\right) \in \left(\mathbb Z\cap [M+1,M+ N]\right)^s$ such that the…

We complete statement and proof for B. Moss\'e's unilateral recognizability theorem. We also provide an algorithm for deciding the unilateral non-recognizability of a given primitive substitution.

This note presents a unified theorem of the alternative that explicitly allows for any combination of equality, componentwise inequality, weak dominance, strict dominance, and nonnegativity relations. The theorem nests 60 special cases,…

In this short note we give counterexamples to several results related to extension theorems published recently.

We introduce elliptic hypertoric varieties, which is an elliptic analogue of hypertoric varieties and multiplicative hypertoric varieties. We also prove an elliptic version of Hikita conjecture, which relates elliptic (resp. additive and…

We provide a complete proof of an optimal version of the Marcinkiewicz multiplier theorem.

Many theorems of mathematics have the form that for a certain problem, e.g. a differential equation or polynomial (in)equality, there exists a solution. The sequential version then states that for a sequence of problems, there is a sequence…

We find a generalization of the Mordell integral and we also establish a set of properties for a generalization of the Mordell integral similar to those in the third author's PhD thesis.

In this note, we give an exposition of the construction of Seiberg-Witten invariants.

A vector variational principle is proved.