Aditya Karnataki

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20212026

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math.NT2026

Explicit isomorphisms for a Herr-type complex over a metabelian extension

Anand Chitrao, Aditya Karnataki, Jishnu Ray

Let $S$ be a Banach algebra over $Q_{p}$ whose residue fields are finite extensions of $Q_{p}$ . Given an arithmetic family $V$ of Galois representations, i.e., a fini…

math.NT2025

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning

Priyavrat Deshpande, Aditya Karnataki, Pratiksha Shingavekar

This article presents a comprehensive data-scientific investigation into the arithmetic statistics of congruent number elliptic curves, leveraging a dataset of square-free integers…

math.NT2023

On the Iwasawa invariants of Artin representations

Aditya Karnataki, Anwesh Ray

We study Iwasawa invariants associated to Selmer groups of Artin representations, and criteria for the vanishing of the associated algebraic Iwasawa invariants. The conditions obta…

math.NT2021

Families of Galois representations and $(φ, τ)$ -modules

Aditya Karnataki, Léo Poyeton

Let $p$ be a prime, and let $K$ be a finite extension of $Q_{p}$ , with absolute Galois group $G_{K}$ . Let $π$ be a uniformizer of $K$ and let $K_{\infty}$ be the Kummer ex…

math.NT2021

Level-raising for automorphic forms on $G L_{n}$

Aditya Karnataki

Let $E$ be a CM number field and $F$ its maximal real subfield. We prove a level-raising result for regular algebraic conjugate self-dual automorphic representations of $GL_n(\math…

math.NT2021

Self-dual Artin representations of dimension three (with an appendix by David E. Rohrlich)

Aditya Karnataki, David E. Rohrlich

We give an unconditional proof that self-dual Artin representations of $Q$ of dimension $3$ have density $0$ among all Artin representations of $Q$ of dimension $…

Explicit isomorphisms for a Herr-type complex over a metabelian extension

Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning

On the Iwasawa invariants of Artin representations

Families of Galois representations and (φ,τ)-modules

Level-raising for automorphic forms on GLn​

Self-dual Artin representations of dimension three (with an appendix by David E. Rohrlich)

Families of Galois representations and $(φ, τ)$ -modules

Level-raising for automorphic forms on $G L_{n}$