1 citations · 1 across the 4 of their papers we have counts for
5 papers
Criterion set for diagonal forms of higher degree
Om Prakash
The 290-Theorem of Bhargava-Hanke completely classifies all universal quadratic forms over the rational integers in terms of a finite criterion set: a positive definite quadratic f…
There are consecutive cubic fields with large class numbers, when ordered by discriminant
Vitezslav Kala, Om Prakash
We consider cubic number fields ordered by their discriminants, and show that there exist arbitrarily long sequences that contain only fields with class numbers greater than a give…
On The Roots of Independence Polynomial: Quantifying The Gap
Om Prakash, Vikram Sharma
The independence polynomial of a graph is the generating polynomial corresponding to its independent sets of different sizes. More formally, if denotes the number of i…
Northcott property and universality of higher degree forms
Om Prakash
Let be a totally real number field, a positive integer, and a higher degree form over . We prove that there are at most finitely many totally real extensions o…
There is no 290-Theorem for higher degree forms
Vitezslav Kala, Om Prakash
We study the universality of forms of degrees greater than 2 over rings of integers of totally real number fields. We show that such universal forms always exist, but cannot be cha…