Anwesh Ray

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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

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.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.NT2022

On the corank of the fine Selmer group of an elliptic curve over a $Z_{p}$ -extension

Anwesh Ray

Let $p$ be an odd prime and $F_{\infty}$ be a $Z_{p}$ -extension of a number field $F$ . Given an elliptic curve $E$ over $F$ , we study the structure of the fine Selmer group ov…

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…

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

Statistics for Iwasawa invariants of elliptic curves, III

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

On the corank of the fine Selmer group of an elliptic curve over a Zp​-extension

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

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

Statistics for Iwasawa invariants of elliptic curves, $III$

On the corank of the fine Selmer group of an elliptic curve over a $Z_{p}$ -extension

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