M. Bhargava

activity

20102026

most citedThe average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point

63 citations · 557 across the 46 of their papers we have counts for

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Showing 2026Show all

3 papers · 1 filter

math.NT2026

The existence of small defining polynomials for number fields

Manjul Bhargava, Sameera Vemulapalli

We prove that every number field of degree $n$ and absolute discriminant $D$ has a defining integral polynomial of degree $n$ whose coefficients are all $O_{n} (D)$ in size, thu…

math.NT2026

The existence and uniqueness of magic-faced hypercubes, and applications to Khajuraho most-perfect magic squares, cubes, and hypercubes

Manjul Bhargava

A $magic-lined hypercube$ (or, simply, $magic hypercube$ ) of order $k$ and dimension $n$ is an arrangement of the numbers $1, \dots, k^{n}$ in a $k\times\cdots\times…

math.NT2026

The existence of infinitely many cubic fields with class group of exact 2-rank 1

Manjul Bhargava, Arul Shankar, Artane Siad +1

We show that infinitely many cubic fields have class group of 2-rank 1.