P. Darbar

activity

20162026

most citedA dichotomy for extreme values of zeta and Dirichlet L-functions

2 citations · 4 across the 14 of their papers we have counts for

collaborators

17 papers

math.NT2026

Upper bound for the moment of shifted values of cubic $L$ -functions over function fields

Pranendu Darbar, Sampa Dey, Gopal Maiti

In this paper, we study correlations of shifted values of cubic $L$ -functions over function fields and derive an upper bound for moments of these shifted values in the limit where…

math.NT2026

Large values of $L (σ, χ)$ over sets of characters with small product set

Pranendu Darbar, Bryce Kerr, Marc Munsch +1

We obtain (conditional and unconditional) results on large values of $L$ -functions $L (s, χ)$ in the critical strip $1/2 \leq ℜ s \leq 1$ when the character $χ$ runs through the ra…

math.NT2025

Linear Combinations of Logarithms of $L$ -functions over Function Fields at Microscopic Shifts and Beyond

Fatma Çiçek, Pranendu Darbar, Allysa Lumley

In the function field setting with a fixed characteristic, it was proven by the second and third authors that the values $lo g L (\frac{1}{2}, χ_{D})$ as $D$ varies over…

math.NT2025

On the Distribution and Maximal Behavior of $L (1, χ_{D})$ over Hyperelliptic Curves

Pranendu Darbar

We improve the range of uniformity in the double-exponential decay of the tail of the distribution established by Lumley~\cite{Lumley} for the quadratic Dirichlet $L$ -function $L(1…

math.NT2025

Littlewood's estimates for $L$ -functions in the hyperelliptic ensemble

Emanuel Carneiro, Pranendu Darbar, Mithun Kumar Das +2

We investigate the analogues of certain classical estimates of Littlewood for the Riemann zeta-function in the context of quadratic Dirichlet $L$ -functions over function fields. In…

math.NT2024

Large values of quadratic Dirichlet $L$ -functions

Pranendu Darbar, Gopal Maiti

Assuming the Generalized Riemann Hypothesis (GRH), we utilize the long resonator method to derive $Ω$ -results for the family of quadratic Dirichlet $L$ -functions $L (σ, χ_{d})$ , where…

math.NT2023

Large values of quadratic Dirichlet $L$ -functions over monic irreducible polynomial in $F_{q} [t]$

Pranendu Darbar, Gopal Maiti

We prove an $Ω$ -result for the quadratic Dirichlet $L$ -function $∣ L (1/2, χ_{P}) ∣$ over irreducible polynomials $P$ associated with the hyperelliptic curve of genus $g$ over a fixed f…

math.NT2023

Asymmetric Distribution of Extreme Values of Cubic $L$ -functions at $s = 1$

Pranendu Darbar, Chantal David, Matilde Lalin +1

We investigate the distribution of values of cubic Dirichlet $L$ -functions at $s = 1$ . Following ideas of Granville and Soundararajan for quadratic $L$ -functions, we model the distri…

math.NT2023★ 2 cited

A dichotomy for extreme values of zeta and Dirichlet L-functions

Andriy Bondarenko, Pranendu Darbar, Markus Valås Hagen +2

We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maxi…

math.NT2022

The variance of a general class of multiplicative functions in short intervals

Pranendu Darbar, Mithun Kumar Das

We study a general class of multiplicative functions by establishing a connection between their ``short averages" and ``long average". More precisely, we employ Fourier analysis an…

math.NT2021

Correlation of shifted values of $L$ -functions in the hyperelliptic ensemble

Pranendu Darbar, Gopal Maiti

The moments of quadratic Dirichlet $L$ -functions over function fields have recently attracted much attention with the work of Andrade and Keating. In this article, we establish low…

math.NT2021

Selberg's Central limit theorem for quadratic Dirichlet L-functions over function fields

Pranendu Darbar, Allysa Lumley

In this article, we study the logarithm of the central value $L (\frac{1}{2}, χ_{D})$ in the symplectic family of Dirichlet $L$ -functions associated with the hyperelliptic…

math.NT2019★ 1 cited

Correlation of multiplicative functions over function fields

Pranendu Darbar, Anirban Mukhopadhyay

In this article we study the asymptotic behaviour of the correlation functions over polynomial ring $F_{q} [x]$ . Let $M_{n, q}$ and $P_{n, q}$ be the set…

math.NT2018

Mean values and moments of arithmetic functions over number fields

Jaitra Chattopadhyay, Pranendu Darbar

For an odd integer $d > 1$ and a finite Galois extension $K / Q$ of degree $d$ , G. Lü and Z. Yang \cite{lu3} obtained an asymptotic formula for the mean values of the diviso…

math.NT2018★ 1 cited

Bombieri-type theorem for convolution of arithmetic functions on Number field

Pranendu Darbar, Anirban Mukhopadhyay

Let $K$ be an imaginary quadratic number field of class number one and $O_{K}$ be its ring of integers. We show that, if the arithmetic functions $f, g:\mathcal{O}_K\righta…

math.NT2017

Bounded gaps between product of two primes in imaginary quadratic number fields

Pranendu Darbar, Anirban Mukhopadhyay, G. K. Viswanadham

We study the gaps between products of two primes in imaginary quadratic number fields using a combination of the methods of Goldston-Graham-Pintz-Yildirim \cite{GGPY}, and Maynard…

math.NT2016

Triple Correlations of Multiplicative Functions

Pranendu Darbar

In this paper, we find asymptotic formula for the following sum with explicit error term: \[M_{x}(g_{1}, g_{2}, g_3)=\frac{1}{x}\sum_{n\le x}g_{1}(F_1(n))g_{2}(F_2(n))g_{3} (F_3(n)…

Upper bound for the moment of shifted values of cubic L-functions over function fields

Large values of L(σ,χ) over sets of characters with small product set

Linear Combinations of Logarithms of L-functions over Function Fields at Microscopic Shifts and Beyond

On the Distribution and Maximal Behavior of L(1,χD​) over Hyperelliptic Curves

Littlewood's estimates for L-functions in the hyperelliptic ensemble

Large values of quadratic Dirichlet L-functions

Large values of quadratic Dirichlet L-functions over monic irreducible polynomial in Fq​[t]

Asymmetric Distribution of Extreme Values of Cubic L-functions at s=1

A dichotomy for extreme values of zeta and Dirichlet L-functions

The variance of a general class of multiplicative functions in short intervals

Correlation of shifted values of L-functions in the hyperelliptic ensemble

Selberg's Central limit theorem for quadratic Dirichlet L-functions over function fields

Correlation of multiplicative functions over function fields

Mean values and moments of arithmetic functions over number fields

Bombieri-type theorem for convolution of arithmetic functions on Number field

Bounded gaps between product of two primes in imaginary quadratic number fields

Triple Correlations of Multiplicative Functions

Upper bound for the moment of shifted values of cubic $L$ -functions over function fields

Large values of $L (σ, χ)$ over sets of characters with small product set

Linear Combinations of Logarithms of $L$ -functions over Function Fields at Microscopic Shifts and Beyond

On the Distribution and Maximal Behavior of $L (1, χ_{D})$ over Hyperelliptic Curves

Littlewood's estimates for $L$ -functions in the hyperelliptic ensemble

Large values of quadratic Dirichlet $L$ -functions

Large values of quadratic Dirichlet $L$ -functions over monic irreducible polynomial in $F_{q} [t]$

Asymmetric Distribution of Extreme Values of Cubic $L$ -functions at $s = 1$

Correlation of shifted values of $L$ -functions in the hyperelliptic ensemble