P. Darbar

collaborators

6 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

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.NT2026

Large values of $L (I ¨ , I ¨ )$ for subgroups of characters

Pranendu Darbar, Bryce Kerr, Marc Munsch +1

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

math.NT2025

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

Fatma ÃiÃ§ek, 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 $lo g L (\frac{1}{2}, I ¨ _{D})$ as $D$ varies ove…

math.NT2025

On the Distribution and Maximal Behavior of $L (1, I ¨ _{D})$ 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…

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

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

Large values of L(I¨,I¨) for subgroups of characters

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

On the Distribution and Maximal Behavior of L(1,I¨D​) over Hyperelliptic Curves

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

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

Large values of $L (I ¨ , I ¨ )$ for subgroups of characters

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

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

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