The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields, along with a reduction theory forbinary cubic forms that provides an efficient way to compute equivalence classes of binary cubic forms.Expand

. Let F q be the (cid:12)nite (cid:12)eld with q elements and let A denote the ring of polynomials in one variable with coe(cid:14)cients in F q . Let P be a monic polynomial irreducible in A . We… Expand

Let Fq be the finite field with q elements and let A denote the ring of polynomials in one variable with coefficients in Fq . Let P be a monic polynomial irreducible in A. We obtain a bound for the… Expand

We give a general method for tabulating all cubic functionfields over Fq(t) whose discriminant D has odd degree, or even degreesuch that the leading coefficient of -3D is a non-square in Fq*, up toa… Expand

Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how… Expand

From the functional equation of Riemann's zeta function, new insight is given into Hadamard's product formula and the method can be extended to other meromorphic functions, in the neighborhood of isolated zeros, inspired by the Weierstraß canonical form.Expand

We prove over fields of power series the analogues of several Diophantine approximation results obtained over the field of real numbers. In particular we establish the power series analogue of… Expand

We consider a totally imaginary extension of a real extension of a rational function ﬁeld over a ﬁnite ﬁeld of odd characteristic. We prove that the relative ideal class number one problem for such… Expand