Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on arithmetic progressions modular forms.

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A Course in Arithmetic

Connections, cohomology and the intersection forms of 4-manifolds

Incorporated in this 2003 volume are the first two books in Mukai's series on moduli theory. The notion of a moduli space is central to geometry. However, its influence is not confined there; for example, the theory of moduli spaces is a crucial ingredient in the proof of Fermat's last theorem. Researchers and graduate students working in areas ranging from Donaldson or Seiberg-Witten invariants to more concrete problems such as vector bundles on curves will find this to be a valuable resource. Amongst other things this volume includes an improved presentation of the classical foundations of invarant theory that, in addition to geometers, would be useful to those studying representation theory. This translation gives an accurate account of Mukai's influential Japanese texts.

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An Introduction to Invariants and Moduli

The aim of this book is to provide an introduction to quadratic forms that builds from basics up to the most recent results. Professor Kitaoka is well known for his work in this area, and in this book he covers many aspects of the subject, including lattice theory, Siegel's formula, and some results involving tensor products of positive definite quadratic forms. The reader is required to have only a knowledge of algebraic number fields, making this book ideal for graduate students and researchers wishing for an insight into quadratic forms.

Arithmetic of quadratic forms

1. NUMBERS: RATIONAL, REAL, p-ADIC We present a brief review of some selected topics in p-adic mathematical physics. More details can be found in the references below and the other references are mainly contained therein. We hope that this brief introduction to some aspects of p-adic mathematical physics could be helpful for the readers of the first issue of the journal p-Adic Numbers, Ultrametric Analysis and Applications. The notion of numbers is basic not only in mathematics but also in physics and entire science. Most of modern science is based on mathematical analysis over real and complex numbers. However, it is turned out that for exploring complex hierarchical systems it is sometimes more fruitful to use analysis over p-adic numbers and ultrametric spaces. p-Adic numbers (see, e.g. [1]), introduced by Hensel, are widely used in mathematics: in number theory, algebraic geometry, representation theory, algebraic and arithmetical dynamics, and cryptography.

On p-adic mathematical physics

Let k be a local field, with char(k) ≠ 2. A quadratic space V over k is a finite dimensional vector space together with a non-degenerate quadratic form Q: V → k.The special orthogonal group SO(V) consists of all linear maps T: V → V which satisfy: Q(Tv) = Q(v) for all ν and det T = 1.

A Course in Arithmetic

Citations

Connections, cohomology and the intersection forms of 4-manifolds

An Introduction to Invariants and Moduli

Arithmetic of quadratic forms

On p-adic mathematical physics

On the Decomposition of a Representation of SOn When Restricted to SOn-1

Related Papers (5)

Sphere packings, lattices, and groups

The Arithmetic of Elliptic Curves

An Introduction to the Theory of Numbers

Introduction to analytic number theory

Number Theory