Jitendra Bajpai

activity

20162026

most citedBilateral series and Ramanujan's radial limits

23 citations · 58 across the 23 of their papers we have counts for

collaborators

25 papers

math.NT2026

On the classification of small cyclotomic integers

Jitendra Bajpai, Srijan Das, Kiran S. Kedlaya +1

We give a general classification theorem for cyclotomic algebraic integers with all complex absolute values bounded by a fixed constant $c$ , modeled on the theorem of Cassels which…

math.NT2026

Euler Characteristics of $SL_{4} (Z)$ and $GL_{4} (Z)$ , and their cohomological consequences

Jitendra Bajpai, Taiwang Deng

We compute the homological Euler characteristics of $SL_{4} (Z)$ and $GL_{4} (Z)$ with coefficients in arbitrary irreducible rational highest-weight r…

math.GR2024

A CFSG-free explicit Jordan's theorem over arbitrary fields

Jitendra Bajpai, Daniele Dona

We prove a version of Jordan's classification theorem for finite subgroups of $GL_{n} (K)$ that is at the same time quantitatively explicit, CFSG-free, and valid for arbitr…

math.NT2024

Relative Lie algebra cohomology of SU(2,1) and Eisenstein classes on Picard surfaces

Jitendra Bajpai, Mattia Cavicchi

We consider Picard surfaces, locally symmetric varieties $S_{Γ}$ attached to the Lie group SU(2,1), and we construct explicit differential forms on $S_{Γ}$ representing Eisenstein clas…

math.GR2023

New dimensional estimates for subvarieties of linear algebraic groups

Jitendra Bajpai, Daniele Dona, Harald Andrés Helfgott

For every connected, almost simple linear algebraic group $G \leq GL_{n}$ over a large enough field $K$ , every subvariety $V \subseteq G$ , and every finite generating set $A\…

math.GR2022

Arithmetic Monodromy in Sp(2n)

Jitendra Bajpai, Daniele Dona, Martin Nitsche

Based on a result of Singh--Venkataramana, Bajpai--Dona--Singh--Singh gave a criterion for a discrete Zariski-dense subgroup of Sp(2n,Z) to be a lattice. We adapt this criterion so…

math.GR2022

Thin monodromy in O(5)

Jitendra Bajpai, Martin Nitsche

This article studies the orthogonal hypergeometric groups of degree five. We establish the thinness of 12 out of the 19 hypergeometric groups of type O(3,2) from [4, Table 6]. Some…

math.GR2022

Commentary on Sp(6) hypergeometric groups

Jitendra Bajpai

We study the examples mentioned in [2,Tables A & C] and establish the arithmeticity of four examples of symplectic hypergeometric groups of degree six. Following [2] we know that t…

math.NT2022

Bloch-Beilinson conjectures for Hecke characters and Eisenstein cohomology of Picard surfaces

Jitendra Bajpai, Mattia Cavicchi

We consider certain families of Hecke characters $ϕ$ over a quadratic imaginary field $F$ . According to the Bloch-Beilinson conjectures, the order of vanishing of the $L$ -function…

math.NT2022★ 1 cited

Lifting of vector-valued automorphic forms

Jitendra Bajpai, Subham Bhakta

Recently, the first author [1] showed that the admissible vector-valued automorphic forms lift to the admissible ones. In this article, we study the lifts for the logarithmic vecto…

math.NT2022★ 23 cited

Bilateral series and Ramanujan's radial limits

Jitendra Bajpai, Susie Kimport, Jie Liang +2

Ramanujan's last letter to Hardy explored the asymptotic properties of modular forms, as well as those of certain interesting $q$ -series which he called \emph{mock theta functions}…

math.GR2022

Arithmeticity of Some Hypergeometric Groups

Jitendra Bajpai, Sandip Singh, Shashank Vikram Singh

We show that the hypergeometric groups associated to the pairs of the parameters $(0, 0, \frac{1}{3}, \frac{2}{3})$ , $\left(\frac{1}{2},\frac{1}{2},\frac{1}{4},\frac{3}{4}…

math.GR2021

Thin monodromy in $Sp (4)$ and $Sp (6)$

Jitendra Bajpai, Daniele Dona, Martin Nitsche

We explore the thinness of hypergeometric groups of type $Sp (4)$ and $Sp (6)$ by applying a new approach of computer-assisted ping pong. We prove the thinness of $…

math.GR2021★ 2 cited

Growth estimates and diameter bounds for untwisted classical groups

Jitendra Bajpai, Daniele Dona, Harald Andrés Helfgott

Babai's conjecture states that, for any finite simple non-abelian group $G$ , the diameter of $G$ is bounded by $(lo g ∣ G ∣)^{C}$ for some absolute constant $C$ . We prove that, for an…

math.NT2020

Growth of Fourier coefficients of vector-valued automorphic forms

Jitendra Bajpai, Subham Bhakta, Renan Finder

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…

math.NT2020

Boundary and Eisenstein Cohomology of $G_{2} (Z)$

Jitendra Bajpai, Lifan Guan

In this article, Eisenstein cohomology of the arithmetic group $G_{2} (Z)$ with coefficients in any finite dimensional highest weight irreducible representation has been dete…

math.NT2020

Exponential sums in prime fields for modular forms

Jitendra Bajpai, Subham Bhakta, Victor C. Garcia

The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. Th…

math.GR2020★ 1 cited

Symplectic Hypergeometric Groups of Degree Six

Jitendra Bajpai, Daniele Dona, Sandip Singh +1

Our computations show that there is a total of $40$ pairs of degree six coprime polynomials $f, g$ where $f (x) = (x - 1)^{6}$ , $g$ is a product of cyclotomic polynomials, $g (0) = 1$ and $f,…

math.NT2019

Euler characteristic and cohomology of $Sp_{4} (Z)$ with nontrivial coefficients

Jitendra Bajpai, Ivan Horozov, Matias Moya Giusti

In this article, the cohomology of the arithmetic group $Sp_{4} (Z)$ with coefficients in any finite dimensional highest weight representation $M_{λ}$ have b…

math.NT2018★ 2 cited

Boundary and Eisenstein Cohomology of $SL_{3} (Z)$

Jitendra Bajpai, Günter Harder, Ivan Horozov +1

In this article, several cohomology spaces associated to the arithmetic groups $SL_{3} (Z)$ and $GL_{3} (Z)$ with coefficients in any highest weight r…

math.GR2017★ 21 cited

Graph isomorphisms in quasi-polynomial time

Harald Andrés Helfgott, Jitendra Bajpai, Daniele Dona

Let us be given two graphs $Γ_{1}$ , $Γ_{2}$ of $n$ vertices. Are they isomorphic? If they are, the set of isomorphisms from $Γ_{1}$ to $Γ_{2}$ can be identified with a coset $H \cdot π$ insi…

math.GR2017★ 7 cited

On Orthogonal Hypergeometric Groups of Degree Five

Jitendra Bajpai, Sandip Singh

A computation shows that there are 77 (up to scalar shifts) possible pairs of integer coefficient polynomials of degree five, having roots of unity as their roots, and satisfying t…

math.NT2017

Lifting of Modular Forms

Jitendra Bajpai

The existence and construction of vector-valued modular forms (vvmf) for any arbitrary Fuchsian group $G$ , for any representation $ρ:\mathrm{G} \longrightarrow \mathrm{GL}…

math.GR2016

Commensurability and arithmetic equivalence for orthogonal hypergeometric monodromy groups

Jitendra Bajpai, Sandip Singh, Scott Thomson

We compute invariants of quadratic forms associated to orthogonal hypergeometric groups of degree five. This allows us to determine some commensurabilities between these groups, as…

On the classification of small cyclotomic integers

Euler Characteristics of SL4​(Z) and GL4​(Z), and their cohomological consequences

A CFSG-free explicit Jordan's theorem over arbitrary fields

Relative Lie algebra cohomology of SU(2,1) and Eisenstein classes on Picard surfaces

New dimensional estimates for subvarieties of linear algebraic groups

Arithmetic Monodromy in Sp(2n)

Thin monodromy in O(5)

Commentary on Sp(6) hypergeometric groups

Bloch-Beilinson conjectures for Hecke characters and Eisenstein cohomology of Picard surfaces

Lifting of vector-valued automorphic forms

Bilateral series and Ramanujan's radial limits

Arithmeticity of Some Hypergeometric Groups

Thin monodromy in Sp(4) and Sp(6)

Growth estimates and diameter bounds for untwisted classical groups

Growth of Fourier coefficients of vector-valued automorphic forms

Boundary and Eisenstein Cohomology of G2​(Z)

Exponential sums in prime fields for modular forms

Symplectic Hypergeometric Groups of Degree Six

Euler characteristic and cohomology of Sp4​(Z) with nontrivial coefficients

Boundary and Eisenstein Cohomology of SL3​(Z)

Graph isomorphisms in quasi-polynomial time

On Orthogonal Hypergeometric Groups of Degree Five

Lifting of Modular Forms

Commensurability and arithmetic equivalence for orthogonal hypergeometric monodromy groups

Euler Characteristics of $SL_{4} (Z)$ and $GL_{4} (Z)$ , and their cohomological consequences

Thin monodromy in $Sp (4)$ and $Sp (6)$

Boundary and Eisenstein Cohomology of $G_{2} (Z)$

Euler characteristic and cohomology of $Sp_{4} (Z)$ with nontrivial coefficients

Boundary and Eisenstein Cohomology of $SL_{3} (Z)$