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Solving conics over function fields

Mark van Hoeij, John Cremona (2006)

Journal de Théorie des Nombres de Bordeaux

Let $F$ be a field whose characteristic is not $2$ and $K = F (t)$ . We give a simple algorithm to find, given $a, b, c \in K^{*}$ , a nontrivial solution in $K$ (if it exists) to the equation $a X^{2} + b Y^{2} + c Z^{2} = 0$ . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in $F$ ; hence we obtain a recursive algorithm for solving diagonal conics over $ℚ (t_{1}, \dots, t_{n})$ (using existing algorithms for such equations over $ℚ$ ) and over $𝔽_{q} (t_{1}, \dots, t_{n})$ .

Some methods for evaluating the regulator of a real quadratic function field.

Stein, Andreas, Williams, Hugh C. (1999)

Experimental Mathematics

Some p-adic Galois Representations for Curves in Characteristic p.

Robert C. Valentini (1986)

Mathematische Zeitschrift

Some remarks on the S-unit equation in function fields

Umberto Zannier (1993)

Acta Arithmetica

Some results on p-extensions of local and global fields

Robert Bond (1979)

Acta Arithmetica

Some sporadic groups as Galois groups II

H. Pahlings (1989)

Rendiconti del Seminario Matematico della Università di Padova

Stickelberger Ideals.

Serge Lang, Daniel S. Kubert (1978)

Mathematische Annalen

Structure of semisimple differentials and p-class groups in Zp-extensions.

M.L. Madan, Gabirel D. Villa Salvador (1986/1987)

Manuscripta mathematica

Subfields of the function field of the Deligne-Lusztig curve of Ree type

Emrah Çakçak, Ferruh Özbudak (2004)

Acta Arithmetica

Sums of L-functions over rational function fields

Gautam Chinta, Joel B. Mohler (2010)

Acta Arithmetica

Sums of units in function fields II: The extension problem

Christopher Frei (2011)

Acta Arithmetica

Sur la géométrie de certaines algèbres de quaternions

E.-U. Gekeler (1990)

Journal de théorie des nombres de Bordeaux

Sur la représentation en somme de carrés des polynômes à une indéterminée sur un corps de nombres algébriques

Y. Pourchet (1971)

Acta Arithmetica

Sur la transcendance de la série formelle Π

Jean-Paul Allouche (1990)

Journal de théorie des nombres de Bordeaux

En utilisant le théorème de Christol, Kamae, Mendès France et Rauzy, nous donnons une démonstration élémentaire de la transcendance de la série formelle $Π$ ainsi que d’autres séries formelles à coefficients dans un corps fini.

Currently displaying 221 – 240 of 295

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Displaying 221 – 240 of 295

Solving conics over function fields

Some methods for evaluating the regulator of a real quadratic function field.

Some p-adic Galois Representations for Curves in Characteristic p.

Some remarks on the S-unit equation in function fields

Some results on p-extensions of local and global fields

Some sporadic groups as Galois groups II

Stickelberger Ideals.

Structure of semisimple differentials and p-class groups in Zp-extensions.

Subfields of the function field of the Deligne-Lusztig curve of Ree type

Sums of L-functions over rational function fields

Sums of units in function fields II: The extension problem

Sur la géométrie de certaines algèbres de quaternions

Sur la représentation en somme de carrés des polynômes à une indéterminée sur un corps de nombres algébriques

Sur la transcendance de la série formelle Π

Sur les périodes des nombres quadratiques spécialisés d'une fonction algébrique quadratique "réelle"

Ternary quadratic forms that represent zero: the function field case

The abc-inequality and the generalized Fermat equation in function fields

The annihilation of divisor classes in abelian extensions of the rational function field

The arithmetic of function fields

The Brauer-Siegel theorem for algebraic function fields.

Currently displaying 221 – 240 of 295