Quadratische Körper im Gebiete der höheren Kongruenzen. II.

  title={Quadratische K{\"o}rper im Gebiete der h{\"o}heren Kongruenzen. II.},
  author={Emil Artin},
  journal={Mathematische Zeitschrift},
  • E. Artin
  • Mathematics
  • Mathematische Zeitschrift

Tabulation of cubic function fields via polynomial binary cubic forms

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.


. 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


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

The 2-primary class group of certain hyperelliptic curves

Let q be an odd prime, e a non-square in the finite field Fq with q elements, p(T) an irreducible polynomial in Fq[T] and A the affine coordinate ring of the hyperelliptic curve y2=ep(T) in the (y,

Confirming Mathematical Conjectures by Analogy

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

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