A. Dixit

collaborators

5 papers

math.NT2026

Statistics of the Genus Number of $S_{3} \times C_{q}$ and $D_{4}$ -fields

Anup B. Dixit, Sunil Kumar Pasupulati

The genus number of a number field is a fundamental invariant which measures the contribution of ramification to its ideal class group. In this paper, we establish the statistics f…

math.NT2026

Brauer-Siegel theorem for families of number fields over almost Sn fields

Anup B Dixit

The classical Brauer-Siegel conjecture describes the asymptotic behaviour of the product of the class number and the regulator in families of number fields. All known cases of the…

math.NT2025

How often are $⌊ n^{I^} \pm ⌋$ and $⌊ n^{2} ⌋$ simultaneously primes?

Anup B. Dixit, Nikhil S Kumar

Let $⌊ x ⌋$ denote the greatest integer less than or equal to a real number $x$ . Given real numbers $0 < I^\pm_{1} < I^\pm_{2} < \dots < I^\pm_{k} < 1$ satisfying a certain conditio…

math.NT2025

On points of small height in infinite extensions

Anup B. Dixit, Sushant Kala

In this paper, we introduce the notion of asymptotically positive infinite extensions of $Q$ , in the spirit of the Tsfasman-VlÄduÅ£ theory of asymptotically exact familie…

math.NT2025

A p-adic criterion for Lehmer's conjecture

Anup B. Dixit, Sushant Kala

For a non-zero algebraic number $I^\pm$ of degree $d$ , let $h (I^\pm)$ denote its logarithmic Weil height. It is known that when $h (I^\pm)$ is small, and $d$ is large, the conjugates of $I^\pm$ …

Statistics of the Genus Number of S3​×Cq​ and D4​-fields

Brauer-Siegel theorem for families of number fields over almost Sn fields

How often are ⌊nI^±⌋ and ⌊n2⌋ simultaneously primes?

On points of small height in infinite extensions

A p-adic criterion for Lehmer's conjecture

Statistics of the Genus Number of $S_{3} \times C_{q}$ and $D_{4}$ -fields

How often are $⌊ n^{I^} \pm ⌋$ and $⌊ n^{2} ⌋$ simultaneously primes?