Mohammad Bardestani

activity

20122025

most citedMertens's theorem for splitting primes and more

1 citations · 1 across the 6 of their papers we have counts for

collaborators

13 papers

math.CO2025

Counting $F_{q}$ -points of orbital varieties in ad-nilpotent ideals of type $A_{n}$

Mohammad Bardestani, Keivan Mallahi-Karai, Samrith Ram +1

Let $b_{n} (F_{q})$ denote the Lie algebra of upper triangular $n \times n$ matrices over the finite field $F_{q}$ , and let $u_{n} (F_{q})$ be the ni…

math.GR2022

Polynomiality of the faithful dimension of nilpotent groups over finite truncated valuation rings

Mohammad Bardestani, Keivan Mallahi-Karai, Dzmitry Rumiantsau +1

The faithful dimension of a finite group $G$ over $C$ , denoted by $m_{faithful} (G)$ , is the smallest integer $n$ such that $G$ can be embedde…

math.RT2017

Kirillov's orbit method and polynomiality of the faithful dimension of $p$ -groups

Mohammad Bardestani, Keivan Mallahi-Karai, Hadi Salmasian

Given a finite group $G$ and a field $K$ , the faithful dimension of $G$ over $K$ is defined to be the smallest integer $n$ such that $G$ embeds into $\ma…

math.CO2017

Polynomial configurations in sets of positive upper density over local fields

Mohammad Bardestani, Keivan Mallahi-Karai

Let $F (x) = (f_{1} (x), \dots, f_{m} (x))$ be such that $1, f_{1}, \dots, f_{m}$ are linearly independent polynomials with real coefficients. Based on ideas of Bachoc, DeCorte, Oliveira and Va…

math.RT2016

On equality of ranks of local components of automorphic representations

Mohammad Bardestani, Hadi Salmasian

We prove that the local components of an automorphic representation of an adelic semisimple group have equal rank in the sense defined earlier by the second author. Our theorem is…

math.GR2015

On the chromatic number of structured Cayley graphs

Mohammad Bardestani, Keivan Mallahi-Karai

In this paper, we will study the chromatic number of Cayley graphs of algebraic groups that arise from algebraic constructions. Using Lang-Weil bound and representation theory of f…

math.CO2015

On a generalization of the Hadwiger-Nelson problem

Mohammad Bardestani, Keivan Mallahi-Karai

For a field $F$ and a quadratic form $Q$ defined on an $n$ -dimensional vector space $V$ over $F$ , let $QG_{Q}$ , called the quadratic graph associated to $Q$ , be the graph wi…

math.RT2015

Minimal dimension of faithful representations for $p$ -groups

Mohammad Bardestani, Keivan Mallahi-Karai, Hadi Salmasian

For a group $G$ , we denote by $m_{f ai t h f u l} (G)$ , the smallest dimension of a faithful complex representation of $G$ . Let $F$ be a non-Archimedean local field with the ring of integ…

math.GR2014

Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields

Mohammad Bardestani, Camelia Karimianpour, Keivan Mallahi-Karai +1

Let $F$ be a non-Archimedean local field with the ring of integers $O$ and the prime ideal $p$ and let $G = G (O / p^{n})$ be th…

math.GR2013

On the Erdos-Ko-Rado property for finite Groups

Mohammad Bardestani, Keivan Mallahi-Karai

Let a finite group $G$ act transitively on a finite set $X$ . A subset $S \subseteq G$ is said to be {\it intersecting} if for any $s_{1}, s_{2} \in S$ , the element $s_{1}^{- 1} s_{2}$ has a fix…

math.NT2013★ 1 cited

Mertens's theorem for splitting primes and more

Mohammad Bardestani, Tristan Freiberg

Myriad articles are devoted to Mertens's theorem. In yet another, we merely wish to draw attention to a proof by Hardy, which uses a Tauberian theorem of Landau that "leads to the…

math.GR2012

Quasi-Random profinite groups

Mohammad Bardestani, Keivan Mallahi-Karai

We will investigate quasi-randomness for profinite groups. We will obtain bounds for the mininal degree of non-trivial representations of $\mathrm{SL}_k(\mathbb{Z}/(p^n\mathbb{Z}))…

math.NT2012

The Density of a family of monogenic number fields

Mohammad Bardestani

A monogenic polynomial $f$ is a monic irreducible polynomial with integer coefficients which produces a monogenic number field. For a given prime $q$ , using the Chebotarev density…

Counting Fq​-points of orbital varieties in ad-nilpotent ideals of type An​

Polynomiality of the faithful dimension of nilpotent groups over finite truncated valuation rings

Kirillov's orbit method and polynomiality of the faithful dimension of p-groups

Polynomial configurations in sets of positive upper density over local fields

On equality of ranks of local components of automorphic representations

On the chromatic number of structured Cayley graphs

On a generalization of the Hadwiger-Nelson problem

Minimal dimension of faithful representations for p-groups

Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields

On the Erdos-Ko-Rado property for finite Groups

Mertens's theorem for splitting primes and more

Quasi-Random profinite groups

The Density of a family of monogenic number fields

Counting $F_{q}$ -points of orbital varieties in ad-nilpotent ideals of type $A_{n}$

Kirillov's orbit method and polynomiality of the faithful dimension of $p$ -groups

Minimal dimension of faithful representations for $p$ -groups