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  • Cited by 33
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Baumann, Michael Heinrich 2018. Die k-dimensionale Champagnerpyramide. Mathematische Semesterberichte,

    Ilić Stepić, Angelina and Ognjanović, Zoran 2018. Logics to formalise p-adic valued probability and their applications. International Journal of Parallel, Emergent and Distributed Systems, Vol. 33, Issue. 3, p. 257.

    Lukina, Olga 2018. Arboreal Cantor actions. Journal of the London Mathematical Society,

    Malikiosis, Romanos-Diogenes 2018. Spark deficient Gabor frames. Pacific Journal of Mathematics, Vol. 294, Issue. 1, p. 159.

    Brownawell, W. D. and Masser, D. W. 2017. Zero estimates with moving targets. Journal of the London Mathematical Society, Vol. 95, Issue. 2, p. 441.

    ARENAS-CARMONA, L. BEREND, D. and BERGELSON, V. 2017. An almost mixing of all orders property of algebraic dynamical systems. Ergodic Theory and Dynamical Systems, p. 1.

    Bell, Jason P. Satriano, Matthew and Sierra, Susan J. 2017. On a dynamical Mordell-Lang conjecture for coherent sheaves. Journal of the London Mathematical Society, Vol. 96, Issue. 1, p. 28.

    Bufetov, Alexander I. and Qiu, Yanqi 2017. Ergodic measures on spaces of infinite matrices over non-Archimedean locally compact fields. Compositio Mathematica, Vol. 153, Issue. 12, p. 2482.

    Nishioka, Seiji 2017. Irreducibility of Discrete Painlevé Equation of Type <i>D</i><sub>7</sub><sup>(1)</sup>. Funkcialaj Ekvacioj, Vol. 60, Issue. 3, p. 305.

    Manners, Freddie 2015. A solution to the pyjama problem. Inventiones mathematicae, Vol. 202, Issue. 1, p. 239.

    Kiwi, Jan 2014. Puiseux series dynamics of quadratic rational maps. Israel Journal of Mathematics, Vol. 201, Issue. 2, p. 631.

    Dalawat, Chandan Singh 2012. Serre’s formule de masse in prime degree. Monatshefte für Mathematik, Vol. 166, Issue. 1, p. 73.

    Nishioka, Seiji 2011. Transcendence of solutions of q-Painlevé equation of type $${A^{(1)}_{6}}$$. Aequationes mathematicae, Vol. 81, Issue. 1-2, p. 121.

    Ormsby, Kyle M. 2011. Motivic invariants of p-adic fields. Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology, Vol. 7, Issue. 03, p. 597.

    Luca, Florian and Siksek, Samir 2010. On factorials expressible as sums of at most three Fibonacci numbers. Proceedings of the Edinburgh Mathematical Society, Vol. 53, Issue. 03, p. 747.

    BUTTON, J. O. 2009. FINITE COVERS OF THE INFINITE CYCLIC COVER OF A KNOT. Journal of Knot Theory and Its Ramifications, Vol. 18, Issue. 01, p. 75.

    Bernik, V. Götze, F. and Kukso, O. 2008. On the divisibility of the discriminant of an integral polynomial by prime powers. Lithuanian Mathematical Journal, Vol. 48, Issue. 4, p. 380.

    Fraatz, Robert 2007. On the Computation of Integral Closures of Cyclic Extensions of Function Fields. LMS Journal of Computation and Mathematics, Vol. 10, Issue. , p. 141.

    Maejima, Makoto and Shah, Riddhi 2007. Operator-semistable, operator semi-selfdecomposable probability measures and related nested classes on p-adic vector spaces. Monatshefte für Mathematik, Vol. 151, Issue. 4, p. 293.

    Mustapha, Sami 2006. Gaussian Estimates for Random Walks on Some Unimodular p-adic Groups. Journal of Theoretical Probability, Vol. 19, Issue. 4, p. 773.


Book description

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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