86,297 research outputs found
Crystal constructions in Number Theory
Weyl group multiple Dirichlet series and metaplectic Whittaker functions can
be described in terms of crystal graphs. We present crystals as parameterized
by Littelmann patterns and we give a survey of purely combinatorial
constructions of prime power coefficients of Weyl group multiple Dirichlet
series and metaplectic Whittaker functions using the language of crystal
graphs. We explore how the branching structure of crystals manifests in these
constructions, and how it allows access to some intricate objects in number
theory and related open questions using tools of algebraic combinatorics
Algorithms in algebraic number theory
In this paper we discuss the basic problems of algorithmic algebraic number
theory. The emphasis is on aspects that are of interest from a purely
mathematical point of view, and practical issues are largely disregarded. We
describe what has been done and, more importantly, what remains to be done in
the area. We hope to show that the study of algorithms not only increases our
understanding of algebraic number fields but also stimulates our curiosity
about them. The discussion is concentrated of three topics: the determination
of Galois groups, the determination of the ring of integers of an algebraic
number field, and the computation of the group of units and the class group of
that ring of integers.Comment: 34 page
Genetic Code and Number Theory
Living organisms are the most complex, interesting and significant objects
regarding all substructures of the universe. Life science is regarded as a
science of the 21st century and one can expect great new discoveries in the
near futures. This article contains an introductory brief review of genetic
information, its coding and translation of genes to proteins through the
genetic code. Some theoretical approaches to the modelling of the genetic code
are presented. In particular, connection of the genetic code with number theory
is considered and the role of -adic numbers is underlined.Comment: 15 pages. To apper in "Modern Topics in Science", a book of invited
papers (Eds. R. Constantinescu, G. Djordjevic, Lj. Nesic
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