Anwesh Ray

activity

20152026

most citedRank stability of elliptic curves in certain non-abelian extensions

2 citations · 3 across the 19 of their papers we have counts for

collaborators

20 papers

math.NT2026

Counting number fields with symplectic Galois group

Anwesh Ray

Let $n \geq 1$ and let $ℓ$ be an odd prime. Let $G = PGSp_{2 n} (F_{ℓ})$ or $GSp_{2 n} (F_{ℓ})$ , and fix a faithful transitive permutation represe…

math.NT2025

Distribution questions for isogeny graphs over finite fields

Anwesh Ray

In the first part of the paper, we fix a non-CM elliptic curve $E / Q$ and an odd prime $ℓ$ and investigate the distribution of invariants associated to the $ℓ$ -volcan…

math.NT2025

Counting elliptic curves with prescribed entanglements

Zachary Couvillon, Anwesh Ray

We establish asymptotic lower bounds for the number of elliptic curves over $Q$ with prescribed entanglement of division fields, ordered by naive height. Such elliptic cur…

math.NT2025

An analogue of Kida's formula for Mazur-Tate elements

Naman Pratap, Anwesh Ray

We prove an analogue of Kida's formula for the Iwasawa invariants of the Mazur-Tate elements attached to elliptic curves over $Q$ . Let $p$ be an odd prime and let $L / K$ be…

math.NT2025

Massey products and the Iwasawa theory of fine Selmer groups

Anwesh Ray, R. Sujatha

A central conjecture of Coates and Sujatha predicts that the fine Selmer group of any $p$ -adic Galois representation is cotorsion over the relevant Iwasawa algebra with vanishing $…

math.NT2025

Mazur's growth number conjecture and congruences

Anwesh Ray

Motivated by the work of Greenberg-Vatsal and Emerton-Pollack-Weston, I investigate the extent to which Mazur's conjecture on the growth of Selmer ranks in $Z_{p}$ -extension…

math.NT2025

Selmer stability in families of congruent Galois representations

Anwesh Ray

In this article I study the variation of Selmer groups in families of modular Galois representations that are congruent modulo a fixed prime $p \geq 5$ . Motivated by analogies with…

math.NT2025

Selmer stability for elliptic curves in Galois $ℓ$ -extensions

Siddhi Pathak, Anwesh Ray

We study the behavior of Selmer groups of an elliptic curve $E / Q$ in finite Galois extensions with prescribed Galois group. Fix a prime $ℓ \geq 5$ , a finite group $G$ w…

math.NT2024

Iwasawa theory and ranks of elliptic curves in quadratic twist families

Jeffrey Hatley, Anwesh Ray

We study the distribution of ranks of elliptic curves in quadratic twist families using Iwasawa-theoretic methods, contributing to the understanding of Goldfeld's conjecture. Given…

math.NT2024

Integers that are sums of two cubes in the cyclotomic $Z_{p}$ -extension

Anwesh Ray

Let $n$ be a cubefree natural number and $p \geq 5$ be a prime number. Assume that $n$ is not expressible as a sum of the form $x^{3} + y^{3}$ , where $x, y \in Q$ . In this note, we…

math.NT2024

A Heuristic approach to the Iwasawa theory of elliptic curves

Katharina Müller, Anwesh Ray

Let $E_{/ Q}$ be an elliptic curve and $p$ an odd prime such that $E$ has good ordinary reduction at $p$ and the Galois representation on $E [p]$ is irreducible. Then Greenb…

math.NT2024

Counting rational maps on $P^{1}$ with prescribed local conditions

Khoa D. Nguyen, Anwesh Ray

We explore distribution questions for rational maps on the projective line $P^{1}$ over $Q$ within the framework of arithmetic dynamics, drawing analogies to ellipt…

math.NT2024

Hilbert's tenth problem for families of $Z_{p}$ -extensions of imaginary quadratic fields

Katharina Müller, Anwesh Ray

Via a novel application of Iwasawa theory, we study Hilbert's tenth problem for number fields occurring in $Z_{p}$ -towers of imaginary quadratic fields $K$ . For a odd prime…

math.NT2024

Galois representations over function fields that are ramified at one prime

Anwesh Ray

Let $F_{q}$ be the finite field with $q$ elements, $F := F_{q} (T)$ and $F^{sep}$ a separable closure of $F$ . Set $A$ to denote the polynomial ring $\math…

math.NT2024

Rank distribution in cubic twist families of elliptic curves

Anwesh Ray, Pratiksha Shingavekar

Let $a$ be an integer which is not of the form $n^{2}$ or $- 3 n^{2}$ for $n \in Z$ . Let $E_{a}$ be the elliptic curve with rational $3$ -isogeny defined by $E_{a} : y^{2} = x^{3} + a$ , and $K…

math.NT2024

On Malle's conjecture for the product of symmetric and nilpotent groups

Hrishabh Mishra, Anwesh Ray

Let $G$ be a finite nilpotent group and $n \in {3, 4, 5}$ . Consider $S_{n} \times G$ as a subgroup of $S_{n} \times S_{∣ G ∣} \subset S_{n ∣ G ∣}$ , where $G$ embeds into the second factor of $…

math.NT2024★ 2 cited

Rank stability of elliptic curves in certain non-abelian extensions

Siddhi Pathak, Anwesh Ray

Let $E_{/ Q}$ be an elliptic curve with rank $E (Q) = 0$ . Fix an odd prime $p$ , a positive integer $n$ and a finite abelian extension $K / Q$ with rank $E(K) =…

math.NT2023

The $T$ -adic Galois representation is surjective for a positive density of Drinfeld modules

Anwesh Ray

Let $F_{q}$ be the finite field with $q \geq 5$ elements, $A := F_{q} [T]$ and $F := F_{q} (T)$ . Assume that $q$ is odd and take $∣ \cdot ∣$ to be the absolute value at…

math.NT2023★ 1 cited

Iwasawa theory of fine Selmer groups associated to Drinfeld modules

Anwesh Ray

Let $q$ be a prime power and $F = F_{q} (T)$ be the rational function field over $F_{q}$ , the field with $q$ elements. Let $ϕ$ be a Drinfeld module over $F$ and $\mathfr…

math.AG2015

Syzygies of Line Bundles on GIT Quotients

Krishna Hanumanthu, Anwesh Ray

Let $k$ be an algebraically closed field. Consider a reductive group $G$ over $k$ . Let $X$ be a projective variety over $k$ with a $G$ -action and let $L$ be a very ample $G$ -linear…

Counting number fields with symplectic Galois group

Distribution questions for isogeny graphs over finite fields

Counting elliptic curves with prescribed entanglements

An analogue of Kida's formula for Mazur-Tate elements

Massey products and the Iwasawa theory of fine Selmer groups

Mazur's growth number conjecture and congruences

Selmer stability in families of congruent Galois representations

Selmer stability for elliptic curves in Galois ℓ-extensions

Iwasawa theory and ranks of elliptic curves in quadratic twist families

Integers that are sums of two cubes in the cyclotomic Zp​-extension

A Heuristic approach to the Iwasawa theory of elliptic curves

Counting rational maps on P1 with prescribed local conditions

Hilbert's tenth problem for families of Zp​-extensions of imaginary quadratic fields

Galois representations over function fields that are ramified at one prime

Rank distribution in cubic twist families of elliptic curves

On Malle's conjecture for the product of symmetric and nilpotent groups

Rank stability of elliptic curves in certain non-abelian extensions

The T-adic Galois representation is surjective for a positive density of Drinfeld modules

Iwasawa theory of fine Selmer groups associated to Drinfeld modules

Syzygies of Line Bundles on GIT Quotients

Selmer stability for elliptic curves in Galois $ℓ$ -extensions

Integers that are sums of two cubes in the cyclotomic $Z_{p}$ -extension

Counting rational maps on $P^{1}$ with prescribed local conditions

Hilbert's tenth problem for families of $Z_{p}$ -extensions of imaginary quadratic fields

The $T$ -adic Galois representation is surjective for a positive density of Drinfeld modules