Diophantine Methods, Lattices, And Arithmetic Theory Of Quadratic Forms: International Workshop Banff International Research Station November 13-18, ... Alberta, Canada (contemporary Mathematics)
by Wai Kiu Chan /
2013 / English / PDF
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This volume contains the proceedings of the International Workshop
on Diophantine Methods, Lattices, and Arithmetic Theory of
Quadratic Forms, held November 13-18, 2011, at the Banff
International Research Station, Banff, Alberta, Canada. The
articles in this volume cover the arithmetic theory of quadratic
forms and lattices, as well as the effective Diophantine analysis
with height functions. Diophantine methods with the use of heights
are usually based on geometry of numbers and ideas from lattice
theory. The target of these methods often lies in the realm of
quadratic forms theory. There are a variety of prominent research
directions that lie at the intersection of these areas, a few of
them presented in this volume:* Representation problems for
quadratic forms and lattices over global fields and rings,
including counting representations of bounded height. * Small zeros
(with respect to height) of individual linear, quadratic, and cubic
forms, originating in the work of Cassels and Siegel, and related
Diophantine problems with the use of heights. * Hermite's constant,
geometry of numbers, explicit reduction theory of definite and
indefinite quadratic forms, and various generalisations. * Extremal
lattice theory and spherical designs.
This volume contains the proceedings of the International Workshop
on Diophantine Methods, Lattices, and Arithmetic Theory of
Quadratic Forms, held November 13-18, 2011, at the Banff
International Research Station, Banff, Alberta, Canada. The
articles in this volume cover the arithmetic theory of quadratic
forms and lattices, as well as the effective Diophantine analysis
with height functions. Diophantine methods with the use of heights
are usually based on geometry of numbers and ideas from lattice
theory. The target of these methods often lies in the realm of
quadratic forms theory. There are a variety of prominent research
directions that lie at the intersection of these areas, a few of
them presented in this volume:* Representation problems for
quadratic forms and lattices over global fields and rings,
including counting representations of bounded height. * Small zeros
(with respect to height) of individual linear, quadratic, and cubic
forms, originating in the work of Cassels and Siegel, and related
Diophantine problems with the use of heights. * Hermite's constant,
geometry of numbers, explicit reduction theory of definite and
indefinite quadratic forms, and various generalisations. * Extremal
lattice theory and spherical designs.
