Jyoti Prakash Saha

activity

20142025

most citedOn minimal complements in groups

14 citations · 34 across the 22 of their papers we have counts for

collaborators

24 papers

math.NT2025

Furstenberg--Sárközy theorem over number fields

Dev Ranjan Pandey, Jyoti Prakash Saha

We introduce the notion of intersective polynomials having coefficients in the ring of integers $O_{K}$ of a number field $K$ , and define a notion of upper density of subse…

math.CO2023

On the spectral gap of Cayley graphs

Jyoti Prakash Saha

Let $Γ$ be a Cayley graph, or a Cayley sum graph, or a twisted Cayley graph, or a twisted Cayley sum graph, or a vertex-transitive graph. Suppose $Γ$ is undirected and non-bipartit…

math.CO2023★ 1 cited

A Cheeger inequality for the lower spectral gap

Jyoti Prakash Saha

Let $Γ$ be a Cayley graph, or a Cayley sum graph, or a twisted Cayley graph, or a twisted Cayley sum graph, or a vertex-transitive graph. Denote the degree of $Γ$ by $d$ , its edge…

math.CO2023

On the cop number and the weak Meyniel conjecture for algebraic graphs

Arindam Biswas, Jyoti Prakash Saha

We show that the cop number of the Cayley sum graph of a finite group $G$ with respect to a symmetric subset $S$ is at most twice its degree when the graph is connected, undirected…

math.NT2021

On some local properties of sequences of big Galois representations

S. Aniruddha, Jyoti Prakash Saha

In this article, we prove that for a convergent sequence of residually absolutely irreducible representations of the absolute Galois group of a number field $F$ with coefficients i…

math.CO2021

A spectral bound for vertex-transitive graphs

Arindam Biswas, Jyoti Prakash Saha

For any finite, undirected, non-bipartite, vertex-transitive graph, we establish an explicit lower bound for the smallest eigenvalue of its normalised adjacency operator, which dep…

math.CO2021★ 1 cited

Expansion in Cayley graphs, Cayley sum graphs and their twists

Arindam Biswas, Jyoti Prakash Saha

The Cayley graphs of finite groups are known to provide several examples of families of expanders, and some of them are Ramanujan graphs. Babai studied isospectral non-isomorphic C…

math.GR2020

On non-surjective word maps on $PSL_{2} (F_{q})$

Arindam Biswas, Jyoti Prakash Saha

Jambor--Liebeck--O'Brien showed that there exist non-proper-power word maps which are not surjective on $PSL_{2} (F_{q})$ for infinitely many $q$ . This provided th…

math.CO2020

Spectrum of twists of Cayley and Cayley sum graphs

Arindam Biswas, Jyoti Prakash Saha

Let $G$ be a finite group with $∣ G ∣ \geq 4$ and $S$ be a subset of $G$ . Given an automorphism $σ$ of $G$ , the twisted Cayley graph $C (G, S)^{σ}$ (resp. the twisted Cayley sum graph $C…

math.CO2020★ 1 cited

Asymptotic behaviour of minimal complements

Arindam Biswas, Jyoti Prakash Saha

The notion of minimal complements was introduced by Nathanson in 2011 as a natural group-theoretic analogue of the metric concept of nets. Given two non-empty subsets $W, W^{'}$ in a g…

math.CO2020★ 4 cited

On non-minimal complements

Arindam Biswas, Jyoti Prakash Saha

The notion of minimal complements was introduced by Nathanson in 2011. Since then, the existence or the inexistence of minimal complements of sets have been extensively studied. Re…

math.NT2020★ 1 cited

Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions

Arindam Biswas, Jyoti Prakash Saha

The study of minimal complements in a group or a semigroup was initiated by Nathanson. The notion of minimal complements and being a minimal complement leads to the notion of co-mi…

math.NT2020★ 1 cited

Infinite co-minimal pairs in the integers and integral lattices

Arindam Biswas, Jyoti Prakash Saha

Given two nonempty subsets $A, B$ of a group $G$ , they are said to form a co-minimal pair if $A \cdot B = G$ , and $A^{'} \cdot B ⊊ G$ for any $\emptyset \neq = A^{'} ⊊ A$ …

math.CO2019

A Cheeger type inequality in finite Cayley sum graphs

Arindam Biswas, Jyoti Prakash Saha

Let $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $∣ S ∣ = d$ . We show that if the undirected Cayley sum graph $C_{Σ} (G, S)$ is an expander graph and is non-bi…

math.CO2019★ 7 cited

On additive co-minimal pairs

Arindam Biswas, Jyoti Prakash Saha

A pair of non-empty subsets $(W, W^{'})$ in an abelian group $G$ is an additive complement pair if $W + W^{'} = G$ . $W^{'}$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \foral…

math.CO2019★ 1 cited

Minimal additive complements in finitely generated abelian groups

Arindam Biswas, Jyoti Prakash Saha

Given two non-empty subsets $W, W^{'} \subseteq G$ in an arbitrary abelian group $G$ , $W^{'}$ is said to be an additive complement to $W$ if $W + W^{'} = G$ and it is minimal if no proper subse…

math.NT2019★ 3 cited

Asymptotic complements in the integers

Arindam Biswas, Jyoti Prakash Saha

Let $W \subseteq Z$ be a non-empty subset of the integers. A nonempty set $C \subseteq Z$ is said to be an asymptotic complement to $W$ if $W + C$ contains almost all…

math.CO2018★ 14 cited

On minimal complements in groups

Arindam Biswas, Jyoti Prakash Saha

Let $W, W^{'} \subseteq G$ be nonempty subsets in an arbitrary group $G$ . The set $W^{'}$ is said to be a complement to $W$ if $W W^{'} = G$ and it is minimal if no proper subset of $W^{'}$ is a co…

math.NT2018

The density of ramified primes

Jyoti Prakash Saha

Let $F$ be a number field, $O$ be a domain with fraction field $K$ of characteristic zero and $ρ : Gal (F / F) \to GL_{n} (O)$ be…

math.NT2018

On Frobenius semisimplicity in Hida families

Jyoti Prakash Saha

Let $p \geq 5$ be a prime and $ℓ \neq = p$ be a prime not dividing the tame level of a $p$ -ordinary Hida family. We prove that the actions of the Frobenius element at $ℓ$ on the…

math.NT2018

Distinguishing pure representations by normalized traces

Manish Kumar Pandey, Sudhir Pujahari, Jyoti Prakash Saha

Given two pure representations of the absolute Galois group of an $ℓ$ -adic number field with coefficients in $Q_{p}$ (with $ℓ \neq = p$ ), we show that the Frob…

math.NT2015

Conductors in $p$ -adic families

Jyoti Prakash Saha

Given a Weil-Deligne representation of the Weil group of an $ℓ$ -adic number field with coefficients in a domain $O$ , we show that its pure specializations have the sam…

math.NT2015

Variation of Weyl modules in $p$ -adic families

Jyoti Prakash Saha

Given a Weil-Deligne representation with coefficients in a domain, we prove the rigidity of the structures of the Frobenius-semisimplifications of the Weyl modules associated to it…

math.NT2014

Congruences of algebraic $L$ -functions of motives

Olivier Fouquet, Jyoti Prakash Saha

We develop a framework to investigate conjectures on congruences between the algebraic part of special values of $L$ -functions of congruent motives. We show that algebraic local Eu…

Furstenberg--Sárközy theorem over number fields

On the spectral gap of Cayley graphs

A Cheeger inequality for the lower spectral gap

On the cop number and the weak Meyniel conjecture for algebraic graphs

On some local properties of sequences of big Galois representations

A spectral bound for vertex-transitive graphs

Expansion in Cayley graphs, Cayley sum graphs and their twists

On non-surjective word maps on PSL2​(Fq​)

Spectrum of twists of Cayley and Cayley sum graphs

Asymptotic behaviour of minimal complements

On non-minimal complements

Infinite co-minimal pairs involving lacunary sequences and generalisations to higher dimensions

Infinite co-minimal pairs in the integers and integral lattices

A Cheeger type inequality in finite Cayley sum graphs

On additive co-minimal pairs

Minimal additive complements in finitely generated abelian groups

Asymptotic complements in the integers

On minimal complements in groups

The density of ramified primes

On Frobenius semisimplicity in Hida families

Distinguishing pure representations by normalized traces

Conductors in p-adic families

Variation of Weyl modules in p-adic families

Congruences of algebraic L-functions of motives

On non-surjective word maps on $PSL_{2} (F_{q})$

Conductors in $p$ -adic families

Variation of Weyl modules in $p$ -adic families

Congruences of algebraic $L$ -functions of motives