Hrishabh Mishra

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20222026

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math.NT2024

Integral Hasse principle for Markoff type cubic surfaces

Hrishabh Mishra

We establish new upper bounds on the number of failures of the integral Hasse principle within the family of Markoff type cubic surfaces $x^{2} + y^{2} + z^{2} - x y z = a$ with $∣ a ∣ \leq A$ as…

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.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

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.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…

Integral Hasse principle for Markoff type cubic surfaces

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

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

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

On the number of subrings of Zn of prime power index

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