1 citations · 1 across the 3 of their papers we have counts for
4 papers
On the Ekedahl sieve for the singular locus of the discriminant polynomial
Gaurav Digambar Patil
The Ekedahl sieve is a powerful tool for enumerating arithmetic objects, but traditional formulations relying on inductive steps often yield suboptimal bounds when applied to highl…
Unique decomposition of orders
Gaurav Digambar Patil
We establish a Fundamental Theorem of Orders (FTO), which allows us to express any order (in a number field) uniquely as an intersection of \textit{irreducible orders}. Along this…
Weighted enumeration of number-fields and counting points that take bounded squarefree values along certain polynomials using Pseudo and Sudo maximal orders
Gaurav Digambar Patil
Ekedhal Sieve can be used to count squarefree bounded values of a polynomial closely related to the discriminant polynomial and one can also get a weighted lower bounds for the num…
Weakly Divisible Rings
Gaurav Digambar Patil
We define a new class of rings parameterized by binary forms of a certain type, and give an effective lower bound for the number of such rings whose discriminant is less than a bou…