Anwesh Ray

activity

20182026

most citedStatistics for Iwasawa invariants of elliptic curves

21 citations · 83 across the 51 of their papers we have counts for

collaborators

Showing 2022 · math.NTShow all

11 papers · 2 filters

math.NT2022

On the number of subrings of $Z^{n}$ of prime power index

Hrishabh Mishra, Anwesh Ray

Let $n$ and $k$ be positive integers, and $f_{n} (k)$ (resp. $g_{n} (k)$ ) be the number of unital subrings (resp. unital irreducible subrings) of $Z^{n}$ of index $k$ . The numbers…

math.NT2022

Galois representations ramified at one prime and with suitably large image

Anwesh Ray

Let $p \geq 7$ be a prime and $n > 1$ be a natural number. We show that there exist infinitely many Galois representations $\varrho:Gal(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow GL_{n}(…

math.NT2022★ 3 cited

An analogue of Kida's formula in graph theory

Anwesh Ray, Daniel Vallières

Let $ℓ$ be a rational prime and let $p : Y \to X$ be a Galois cover of finite graphs whose Galois group is a finite $ℓ$ -group. Consider a $Z_{ℓ}$ -tower above…

math.NT2022★ 2 cited

A note on the distribution of Iwasawa invariants of imaginary quadratic fields

Anwesh Ray

Given an odd prime number $p$ and an imaginary quadratic field $K$ , we establish a relationship between the $p$ -rank of the class group of $K$ , and the classical $λ$ -invariant of t…

math.NT2022

Diophantine equations of the form $Y^{n} = f (X)$ over function fields

Anwesh Ray

Let $ℓ$ and $p$ be (not necessarily distinct) prime numbers and $F$ be a global function field of characteristic $ℓ$ with field of constants $κ$ . Assume that there exists a p…

math.NT2022★ 2 cited

Remarks on Hilbert's tenth problem and the Iwasawa theory of elliptic curves

Anwesh Ray

Let $E$ be an elliptic curve with positive rank over a number field $K$ and let $p$ be an odd prime number. Let $K_{cy c}$ be the cyclotomic $Z_{p}$ -extension of $K$ and $K_n…

math.NT2022

Asymptotic growth of Iwasawa invariants in Noncommutative towers of number fields

Anwesh Ray

Let $p$ be an odd prime, $F$ be a number field and consider a uniform infinite pro- $p$ extension $F_{\infty}$ of $F$ with Galois group $G = G a l (F_{\infty} / F)$ . Let \[G=G_0\supset G_1\sup…

math.NT2022

Remarks on Catalan's equation over function fields

Anwesh Ray

Let $ℓ$ be a prime number, $F$ be a global function field of characteristic $ℓ$ . Assume that there is a prime $P_{\infty}$ of degree $1$ . Let $O_{F}$ be the ring of fun…

math.NT2022

Class group statistics for torsion fields generated by elliptic curves

Anwesh Ray, Tom Weston

For a prime $p$ and a rational elliptic curve $E_{/ Q}$ , set $K = Q (E [p])$ to denote the torsion field generated by $E [p] := ker {E p E}$ .…

math.NT2022

Topological Iwasawa invariants and Arithmetic Statistics

Cedric Dion, Anwesh Ray

Given a prime number $p$ , we study topological analogues of Iwasawa invariants associated to $Z_{p}$ -covers of the $3$ -sphere that are branched along a link. We prove explic…

math.NT2022★ 1 cited

On the $μ$ equals zero conjecture for the fine Selmer group in Iwasawa theory

Shaunak V. Deo, Anwesh Ray, R. Sujatha

We study the Iwasawa theory of the fine Selmer group associated to certain Galois representations. The vanishing of the $μ$ -invariant is shown to follow in some cases from a natura…

On the number of subrings of Zn of prime power index

Galois representations ramified at one prime and with suitably large image

An analogue of Kida's formula in graph theory

A note on the distribution of Iwasawa invariants of imaginary quadratic fields

Diophantine equations of the form Yn=f(X) over function fields

Remarks on Hilbert's tenth problem and the Iwasawa theory of elliptic curves

Asymptotic growth of Iwasawa invariants in Noncommutative towers of number fields

Remarks on Catalan's equation over function fields

Class group statistics for torsion fields generated by elliptic curves

Topological Iwasawa invariants and Arithmetic Statistics

On the μ equals zero conjecture for the fine Selmer group in Iwasawa theory

On the number of subrings of $Z^{n}$ of prime power index

Diophantine equations of the form $Y^{n} = f (X)$ over function fields

On the $μ$ equals zero conjecture for the fine Selmer group in Iwasawa theory