ERROR ESTIMATES FOR THE DAVENPORT-HEILBRONN THEOREMS (2008)
Karim Belabas, Manjul Bhargava, Carl Pomerance
Abstract. We improve the known remainder terms for the theorems of Davenport and Heilbronn on the density of discriminants of cubic fields and average 3-torsion in the class group of quadratic...
Using Serre's mass formula [15] for totally ramified extensions, we derive a mass formula that counts all (isomorphism classes of) étale algebra extensions of a local field F having a given degree...
The density of discriminants of quartic rings and fields (2005)
The primary purpose of this article is to prove the following theorem.
Factoring Dickson polynomials over finite fields (1999)
Manjul Bhargava, Michael Zieve
We derive the factorizations of the Dickson polynomials Dn(X, a) and En(X, a), and of the bivariate Dickson polynomials Dn(X, a) − Dn(Y, a), over any finite field. Our proofs are significantly...
Factoring Dickson polynomials over finite fields (1997)
Manjul Bhargava, Michael Zieve
We derive the factorizations of the Dickson polynomials D n (X; a) and E n (X; a), and of the bivariate Dickson polynomials D n (X; a) \Gamma D n (Y; a), over any finite field. Our proofs are...
On P-orderings and polynomial functions on arbitrary subsets of dedekind-type rings / (1996)
Thesis (A.B., Honors in Mathematics) --Harvard University, 1996.