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                                                    3. Local Fields
                                                  2. Cited by 101
                                                  3. Cited by
                                                    Crossref Citations
                                                    Crossref logo
                                                    This Book has been cited by the following publications. This list is generated based on data provided by Crossref.
                                                    Grunewald, F. J. Segal, D. and Smith, G. C. 1988. Subgroups of finite index in nilpotent groups. Inventiones Mathematicae, Vol. 93, Issue. 1, p. 185.
                                                    Calderbank, A. R. and Morton, Patrick 1990. Quasi-Symmetric 3-Designs and Elliptic Curves. SIAM Journal on Discrete Mathematics, Vol. 3, Issue. 2, p. 178.
                                                    Shah, Riddhi 1991. Infinitely divisible measures onp-adic groups. Journal of Theoretical Probability, Vol. 4, Issue. 2, p. 391.
                                                    Dani, S. G. and Shah, Riddhi 1991. Contraction subgroups and semistable measures on p-adic Lie groups. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 110, Issue. 2, p. 299.
                                                    Evans, Steven N. 1993. Local field brownian motion. Journal of Theoretical Probability, Vol. 6, Issue. 4, p. 817.
                                                    Shah, Riddhi 1993. Semistable measures and limit theorems on real andp-adic groups. Monatshefte f�r Mathematik, Vol. 115, Issue. 3, p. 191.
                                                    Flath, Dan and Peele, Rhodes 1993. Applications of Fibonacci Numbers. p. 221.
                                                    Hoffmann, Detlev W. 1994. The Newton polygon of a product of power series. Manuscripta Mathematica, Vol. 85, Issue. 1, p. 109.
                                                    Chiswell, I. M. 1995. Semigroups, Formal Languages and Groups. p. 255.
                                                    Rudolph, Daniel J. and Schmidt, Klaus 1995. Almost block independence and bernoullicity of ? d -actions by automorphisms of compact abelian groups. Inventiones Mathematicae, Vol. 120, Issue. 1, p. 455.
                                                    Myerson, G. and van der Poorten, A. J. 1995. Some Problems Concerning Recurrence Sequences. The American Mathematical Monthly, Vol. 102, Issue. 8, p. 698.
                                                    Ishida, Nobuhiko and Ishii, Noburo 1996. The equations for modular function fields of principal congruence subgroups of prime level. Manuscripta Mathematica, Vol. 90, Issue. 1, p. 271.
                                                    Daberkow, M. and Pohst, M. 1996. On integral bases in relative quadratic extensions. Mathematics of Computation, Vol. 65, Issue. 213, p. 319.
                                                    Cartwright, Donald I. and Steger, Tim 1998. Application of the Bruhat-Tits tree of SU3(h) to some Ã2 groups. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 64, Issue. 3, p. 329.
                                                    Sally, Paul J. 1998. An Introduction to p-adic Fields, Harmonic Analysis and the Representation Theory of SL2 . Letters in Mathematical Physics, Vol. 46, Issue. 1, p. 1.
                                                    Wang, Chin-Lung 1998. On the topology of birational minimal models. Journal of Differential Geometry, Vol. 50, Issue. 1,
                                                    Choi, Kwok-Kwong 1999. On the distribution of points in projective space of bounded height. Transactions of the American Mathematical Society, Vol. 352, Issue. 3, p. 1071.
                                                    Gao, Shuhong and Shokrollahi, M. Amin 2000. Coding Theory and Cryptography. p. 214.
                                                    Cantor, David G. and Gordon, Daniel M. 2000. Algorithmic Number Theory. Vol. 1838, Issue. , p. 185.
                                                    Flynn, E. Victor 2000. Algorithmic Number Theory. Vol. 1838, Issue. , p. 65.
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                                                    Subjects:
                                                    Mathematics (general), Mathematics, Number Theory, Algebra
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                                                    The p-adic numbers, the earliest of local fields, were introduced by Hensel some 70 years ago as a natural tool in algebra number theory. Today the use of this and other local fields pervades much of mathematics, yet these simple and natural concepts, which often provide remarkably easy solutions to complex problems, are not as familiar as they should be. This book, based on postgraduate lectures at Cambridge, is meant to rectify this situation by providing a fairly elementary and self-contained introduction to local fields. After a general introduction, attention centres on the p-adic numbers and their use in number theory. There follow chapters on algebraic number theory, diophantine equations and on the analysis of a p-adic variable. This book will appeal to undergraduates, and even amateurs, interested in number theory, as well as to graduate students.

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