• Corpus ID: 3547010

# QUADRATIC FORMS OVER GLOBAL FIELDS

```@inproceedings{Clark2012QUADRATICFO,
author={Pete L. Clark},
year={2012}
}```
1. The Hasse Principle(s) For Quadratic Forms Over Global Fields 1 1.1. Reminders on global fields 1 1.2. Statement of the Hasse Principles 2 2. The Hasse Principle Over Q 3 2.1. Preliminary Results: Reciprocity and Approximation 3 2.2. n ≤ 1 6 2.3. n = 2 6 2.4. n = 3 6 2.5. n = 4 8 2.6. n ≥ 5 9 3. The Hasse Principle Over a Global Field 9 3.1. n = 2 10 3.2. n = 3 10 3.3. n = 4 11 3.4. n ≥ 5 12 4. Some Applications to Integral Forms 12 4.1. The Aubry-Davenport-Cassels Lemma 12 4.2. Two, Three…

## References

SHOWING 1-10 OF 20 REFERENCES
Historically the theory of quadratic forms has its origins in number-theoretic questions of the following type: Which integers can be written in the form x 2 + 2y 2 , which are sums of three squares,
A brief classical introduction Quadratic spaces and lattices Valuations, local fields, and \$p\$-adic numbers Quadratic spaces over \$\mathbb{Q}_p\$ Quadratic spaces over \$\mathbb{Q}\$ Lattices over
Number Theory: An Introduction to Mathematics
Preface.- The Expanding Universe of Numbers.- Divisibility.- More on Divisibility.- Continued Fractions and their Uses.- Hadamard's Determinant Problem.-Hensel's P-Adic Numbers.- Notations.- Axioms.-
• P. Clark
• Mathematics, Computer Science
• 2012
The notion of a Euclidean quadratic form over a normed integral domain and an ADC form over an integral domain are defined and the study and classification of these two classes ofquadratic forms are initiated, especially over discrete valuation rings and Hasse domains.
A Course in Arithmetic
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
An Introduction to the Theory of Numbers
• E. T.
• Mathematics
Nature
• 1946
THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.
An Introduction to the Theory of Numbers, Sixth Edition
• Psychology
• 2008
Read more and get great! That's what the book enPDFd an introduction to the theory of numbers 5th edition will give for every reader to read this book. This is an on-line book provided in this
Algebraische Theorie der Körper
----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung