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

Showing 2024Show all

9 papers · 1 filter

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) =…

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

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