ﻻ يوجد ملخص باللغة العربية
Let $G$ be a finite (not necessarily abelian) group and let $p=p(G)$ be the smallest prime number dividing $|G|$. We prove that $d(G)leq frac{|G|}{p}+9p^2-10p$, where $d(G)$ denotes the small Davenport constant of $G$ which is defined as the maximal integer $ell$ such that there is a sequence over $G$ of length $ell$ contains no nonempty one-product subsequence.
Let $cO_K$ be a complete discrete valuation ring of residue characteristic $p>0$, and $G$ be a finite flat group scheme over $cO_K$ of order a power of $p$. We prove in this paper that the Abbes-Saito filtration of $G$ is bounded by a simple linear f
Let $D subset mathbb{R}^d$ be a bounded, connected domain with smooth boundary and let $-Delta u = mu_1 u$ be the first nontrivial eigenfunction of the Laplace operator with Neumann boundary conditions. We prove $$ |u|_{L^{infty}(D)} leq 60 cdot |u|_
We prove a conjecture of the first-named author ([J14]) on the upper bound Fourier coefficients of automorphic forms in Arthur packets of split classical groups over any number field.
Let $G$ be a finite abelian group of exponent $n$, written additively, and let $A$ be a subset of $mathbb{Z}$. The constant $s_A(G)$ is defined as the smallest integer $ell$ such that any sequence over $G$ of length at least $ell$ has an $A$-weighted
For a finite group $G$, let $mathrm{diam}(G)$ denote the maximum diameter of a connected Cayley graph of $G$. A well-known conjecture of Babai states that $mathrm{diam}(G)$ is bounded by ${(log_{2} |G|)}^{O(1)}$ in case $G$ is a non-abelian finite si