63 citations · 557 across the 46 of their papers we have counts for
53 papers
The existence of small defining polynomials for number fields
Manjul Bhargava, Sameera Vemulapalli
We prove that every number field of degree and absolute discriminant has a defining integral polynomial of degree whose coefficients are all in size, thu…
The existence and uniqueness of magic-faced hypercubes, and applications to Khajuraho most-perfect magic squares, cubes, and hypercubes
Manjul Bhargava
A (or, simply, ) of order and dimension is an arrangement of the numbers in a $k\times\cdots\times…
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.
The second moment of the size of the -class group of monogenized cubic fields
Manjul Bhargava, Arul Shankar, Ashvin Swaminathan
We prove that when totally real (resp., complex) monogenized cubic number fields are ordered by height, the second moment of the size of the -class group is at most (resp.,…
A proof of van der Waerden's Conjecture on random Galois groups of polynomials
Manjul Bhargava
Of the monic integer polynomials with , how many have associated Galois group that is not the full sy…
Integers expressible as the sum of two rational cubes
Levent Alpöge, Manjul Bhargava, Ari Shnidman
We prove that a positive proportion of integers are expressible as the sum of two rational cubes, and a positive proportion are not so expressible, thus proving a conjecture of Dav…