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Cyclotomic modular lattices

Eva Bayer-Fluckiger (2000)

Journal de théorie des nombres de Bordeaux

Several interesting lattices can be realised as ideal lattices over cyclotomic fields : some of the root lattices, the Coxeter-Todd lattice, the Leech lattice, etc. Many of these are modular in the sense of Quebbemann. The aim of the present paper is to determine the cyclotomic fields over which there exists a modular ideal lattice. We then study an especially simple class of lattices, the ideal lattices of trace type. The paper gives a complete list of modular ideal lattices of trace type defined...

Cyclotomic quadratic forms

François Sigrist (2000)

Journal de théorie des nombres de Bordeaux

Voronoï ’s algorithm is a method for obtaining the complete list of perfect n -dimensional quadratic forms. Its generalization to G -forms has the advantage of running in a lower-dimensional space, and furnishes a finite, and complete, classification of G -perfect forms ( G is a finite subgroup of G L ( n , ℤ ) ) . We study the standard, φ ( m ) -dimensional irreducible representation of the cyclic group C m of order m , and give the, often new, densest G -forms. Perfect cyclotomic forms are completely classified for φ ( m ) < 16 and for...

Décomposition des nombres premiers dans des extensions non abéliennes

Philippe Satge (1977)

Annales de l'institut Fourier

Soit K un corps de nombre galoisien non abélien sur Q dont le groupe de Galois G possède un sous-groupe abélien distingué H vérifiant les propriétés suivantes : l’ordre de H est impair si son corps des invariants est un corps réel de degré strictement supérieur à 2, et l’application transfert qui lui est associée est l’application triviale. On montre que la décomposition d’un nombre premier dans une telle extension dépend de la représentation de ce nombre par certaines formes à coefficients entiers...

Decompositions of an Abelian surface and quadratic forms

Shouhei Ma (2011)

Annales de l’institut Fourier

When a complex Abelian surface can be decomposed into a product of two elliptic curves, how many decompositions does the Abelian surface admit? We provide arithmetic formulae for the number of such decompositions.

Currently displaying 161 – 180 of 1236