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

54 papers

math.NT2026

Iwasawa theory of class field towers

Anwesh Ray

Let $p$ be an odd prime and let $K_{\infty} / K$ be a $Z_{p}$ -extension. For each finite layer $K_{n}$ , let $G_{n}$ be the Galois group of its maximal unramified pro- $p$ extension.…

math.NT2026

Local-global principles for visibility of lattice points on parameterized curves

Sneha Chaubey, Anwesh Ray

We develop a local-global theory for visibility of lattice points on families of parameterized curves. We introduce a notion of $p$ -adic visibility and ask whether a lattice point…

math.NT2026

Galois representations ramified at one prime via relative deformation theory

Anwesh Ray

Let $p$ be an odd prime and let $G / Z$ be a split connected reductive group with $dim Z (G) \leq 1$ . Assume that a split maximal torus of $\mat…

math.NT2026

Cyclotomic norm congruences for zeta values and modular $L$ -values

Shubhrajit Bhattacharya, Anwesh Ray, R. Sujatha

We study congruences between special values of zeta functions and modular $L$ -functions in cyclotomic towers. The underlying mechanism is an integral norm congruence for finite-lev…

math.NT2026

Greenberg's $μ = 0$ conjecture for lisse sheaves over global function fields

Anwesh Ray

Let $K$ be a global function field of characteristic $p > 0$ and $ℓ \neq = p$ be a prime number. We study Selmer groups over a $Z_{ℓ}$ -extension $K_{\infty} / K$ . For a lisse $…

math.NT2024

Galois representations are surjective for almost all Drinfeld modules

Anwesh Ray

This article advances the results of Duke on the average surjectivity of Galois representations for elliptic curves to the context of Drinfeld modules over function fields. Let $F$ …

math.NT2024

Statistics for Iwasawa invariants of elliptic curves, $III$

Anwesh Ray

Given a prime $p \geq 5$ , a conjecture of Greenberg predicts that the $μ$ -invariant of the $p$ -primary Selmer group should vanish for most elliptic curves with good ordinary reducti…

math.NT2024★ 1 cited

An analogue of Kida's formula for elliptic curves with additive reduction

Anwesh Ray, Pratiksha Shingavekar

We study the Iwasawa theory of $p$ -primary Selmer groups of elliptic curves $E$ over a number field $K$ . Assume that $E$ has additive reduction at the primes of $K$ above $p$ . In t…

math.NT2023

Upper bounds for the number of number fields with prescribed Galois group

Hrishabh Mishra, Anwesh Ray

Let $n$ be a positive integer and $G$ be a transitive permutation subgroup of $S_{n}$ . Given a number field $K$ with $[K : Q] = n$ , we let $K$ be its Galois closure…

math.NT2023

Asymptotic growth patterns for class field towers

Arindam Bhattacharyya, Vishnu Kadiri, Anwesh Ray

Let $p$ be an odd prime number. We study growth patterns associated with finitely ramified Galois groups considered over the various number fields varying in a $Z_{p}$ -tower…

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.NT2023

Remarks on Greenberg's conjecture for Galois representations associated to elliptic curves

Anwesh Ray

Let $E_{/ Q}$ be an elliptic curve and $p$ be an odd prime number at which $E$ has good ordinary reduction. Let $S e l_{p^{\infty}} (Q_{\infty}, E)$ denote the $p$ -primar…

math.NT2023

Counting number fields whose Galois group is a wreath product of symmetric groups

Hrishabh Mishra, Anwesh Ray

Let $K$ be a number field and $k \geq 2$ be an integer. Let $(n_{1}, n_{2}, \dots, n_{k})$ be a vector with entries $n_{i} \in Z_{\geq 2}$ . Given a number field extension $L / K$ , we d…

math.NT2023

Lower bounds for the number of number fields with Galois group $G L_{2} (F_{ℓ})$

Anwesh Ray

Let $ℓ \geq 5$ be a prime number and $F_{ℓ}$ denote the finite field with $ℓ$ elements. We show that the number of Galois extensions of the rationals with Galois gro…

math.NT2023

Diophantine stability for elliptic curves on average

Anwesh Ray, Tom Weston

Let $K$ be a number field and $ℓ \geq 5$ a prime number. Mazur and Rubin introduced the notion of diophantine stability for a variety $X_{/ K}$ at a prime $ℓ$ . We show that th…

math.CO2023

On the distribution of eigenvalues in families of Cayley graphs

Matilde Lalin, Anwesh Ray

We consider the family of undirected Cayley graphs associated with odd cyclic groups, and study statistics for the eigenvalues in their spectra. Our results are motivated by analog…

math.NT2023

Constructing Galois representations with prescribed Iwasawa $λ$ -invariant

Anwesh Ray

Let $p \geq 5$ be a prime number. We consider the Iwasawa $λ$ -invariants associated to modular Bloch-Kato Selmer groups, considered over the cyclotomic $Z_{p}$ -extension of $…

math.NT2023★ 1 cited

Hilbert's tenth problem in Anticyclotomic towers of number fields

Anwesh Ray, Tom Weston

Let $K$ be an imaginary quadratic field and $p$ be an odd prime which splits in $K$ . Let $E_{1}$ and $E_{2}$ be elliptic curves over $K$ such that the $G a l (K ˉ / K)$ -modules $E_{1} [p]$ …

math.GT2022

On the distribution of Alexander polynomials in certain families of closed braids

Anwesh Ray

We study the distribution of arithmetic invariants associated to Alexander polynomials for certain infinite families of links. The families of links we consider arise from braids o…

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…

Iwasawa theory of class field towers

Local-global principles for visibility of lattice points on parameterized curves

Galois representations ramified at one prime via relative deformation theory

Cyclotomic norm congruences for zeta values and modular L-values

Greenberg's μ=0 conjecture for lisse sheaves over global function fields

Galois representations are surjective for almost all Drinfeld modules

Statistics for Iwasawa invariants of elliptic curves, III

An analogue of Kida's formula for elliptic curves with additive reduction

Upper bounds for the number of number fields with prescribed Galois group

Asymptotic growth patterns for class field towers

On the Iwasawa invariants of Artin representations

Remarks on Greenberg's conjecture for Galois representations associated to elliptic curves

Counting number fields whose Galois group is a wreath product of symmetric groups

Lower bounds for the number of number fields with Galois group GL2​(Fℓ​)

Diophantine stability for elliptic curves on average

On the distribution of eigenvalues in families of Cayley graphs

Constructing Galois representations with prescribed Iwasawa λ-invariant

Hilbert's tenth problem in Anticyclotomic towers of number fields

On the distribution of Alexander polynomials in certain families of closed braids

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

Cyclotomic norm congruences for zeta values and modular $L$ -values

Greenberg's $μ = 0$ conjecture for lisse sheaves over global function fields

Statistics for Iwasawa invariants of elliptic curves, $III$

Lower bounds for the number of number fields with Galois group $G L_{2} (F_{ℓ})$

Constructing Galois representations with prescribed Iwasawa $λ$ -invariant

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

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