Tabulation of cubic function fields via polynomial binary cubic forms
- Mathematics, Computer ScienceMath. Comput.
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.
ON CERTAIN CHARACTER SUMS OVER F q [ T ]
. 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…
ON CERTAIN CHARACTER SUMS OVER
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…
Tabulation of Cubic Function Fields with Imaginary and Unusual Hessian
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…
Confirming Mathematical Conjectures by Analogy
- Philosophy, Mathematics
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…
An Analytical and Numerical Detour for the Riemann Hypothesis
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.
On homogeneous and inhomogeneous Diophantine approximation over the fields of formal power series
- MathematicsPacific Journal of Mathematics
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…
Class number in non Galois quartic and non abelian Galois octic function ﬁelds over ﬁnite ﬁelds
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…