P-adic functional analysis pdf

Compared to other books on the subject, its novelty is both a particularly balanced approach to these three points of view and an emphasis on topics accessible to undergraduates. Some of the features which are not treated in other introductory p adic analysis texts are topological models of p adic spaces inside euclidean space, a construction of spherically complete fields, a p adic mean value theorem and some consequences, a special case of hazewinkels functional equation lemma, a remainder formula for the mahler. Buy padic numbers, padic analysis, and zetafunctions graduate texts in mathematics v. Sorry, we are unable to provide the full text but you may find it at the following locations. In many ways p adic analysis is less subtle than classical analysis, since the ultrametric inequality means, for example, that convergence of infinite series of p adic numbers is much simpler. Nonarchimedean functional analysis, where alternative but equally valid number systems such as p adic numbers are fundamental, is a fastgrowing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. A polynomial fx 2f qx is called a permutation polynomial over f q if fx induces a oneone map of f. Pictures of ultrametric spaces, the padic numbers, and. A presentation of results in p adic banach spaces, spaces over fields with an infinite rank valuation, frechet and locally convex spaces with schauder bases, function spaces, p adic harmonic analysis, and related areas. For further interesting examples of ultrametric spaces in the context of trees, see 5. It is an extension of q, so the temptation is to imagine q. Introduction let f q be the nite eld of q elements, where q pr. Citescore values are based on citation counts in a given year e. Advances in ultrametric analysis american mathematical society.

Advances in nonarchimedean analysis american mathematical. The book gives an introduction to \ p\ adic numbers from the point of view of number theory, topology, and analysis. Padic functional analysis lecture notes in pure and. Neal koblitz treats the shnirelman integral in his book padic analysis. Some applications have required the development of p adic functional analysis and spectral theory. Part i background from padic functional analysis throughout this course kis a nite extension of the eld q p of padic numbers, jjdenotes the absolute value on k, o kthe ring of integers.

Since a functional calculus of an operator over the residue. Nov, 2014 we consider summation of some finite and infinite functional p adic series with factorials. Lectures on some aspects of padic analysis school of. Kakol adam mickiewicz university poznan, poland marcel dekker, inc. Non archimedean functional analysis download ebook pdf.

However, here we wish to relay another, deeper, relation between the cohomology. Contains research articles by nearly 40 leading mathematicians from north and south america, europe, africa, and asia, presented at the fourth international conference on p adic functional analysis held recently in nijmegen, the netherlands. The valued field qp of padic numbers is nonarchimedean and spherically complete. In the latter half of the 20th century, this restricted viewpoint was enlarged through the foundational work of kubota and leopoldt and later by iwasawa who established much of the groundwork of a p adic analytic number theory. Periods on the lubintate moduli space tex, dvi, pdf, ps see also. On the other hand, such p adic dynamical systems appear in the process of studying p adic gibbs measures 11, 16, 17, 26. Thus, the search for p adic incarnations of the classical zeta. Ii representations of classical groups over padic fields 43. Therefore, naturally there arises a need to study the dynamics of these functions in the p adic analysis. These notes are essentially the lecture notes for that course.

Let k be an algebraically closed field of characteristic zero, complete for an ultrametric absolute value. In order to avoid from the analysis, we studya relation between reductions, spectra, and functional calculi. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. A presentation of results in padic banach spaces, spaces over fields with an infinite rank valuation, frechet and locally convex spaces with schauder bases, function spaces, padic harmonic analysis, and related areas. The present studies are part of a larger project, the goal of which is to transfer the main ideas of infinitedimensional real differential calculus and nonlinear functional analysis into non. As a function of x, the coefficient cn is a polynomial of degree at most n. Introduction to p adic analytic number theory download. A padic lifting lemma and its application to permutation. Sch02 schneider, peter, nonarchimedean functional analysis. By the way, discretely valued fields like adic number fields. Aspects of padic nonlinear functional analysis request pdf. Bruhat notes by sunder lal no part of this book may be reproduced in any form by print, micro.

Click download or read online button to get introduction to p adic analytic number theory book now. It showcases research results in functional analysis over nonarchimedean value. A p adic lifting lemma and its application to permutation polynomials daqing wan department of mathematical sciences university of nevada, las vegas las vegas, nevada 89154 0. Padic functional analysis lecture notes in pure and applied. In this paper, we present rather large class of such p adic functional series with integer coefficients which contain factorials. Various theorems in elementary p adic analysis, commonly proved only for. Kx, f, g are meromorphic functions in k, or in an open disk, g satisfying conditions on the order of its zeros and poles. Turning information modulo one power of pinto similar information modulo a higher power of pcan be interpreted as improving an approximation. May 31, 2000 some of the features which are not treated in other introductory p adic analysis texts are topological models of p adic spaces inside euclidean space, a construction of spherically complete fields, a p adic mean value theorem and some consequences, a special case of hazewinkels functional equation lemma, a remainder formula for the mahler. Pdf summation of a large class of the functional series, which terms contain factorials, is considered. It showcases research results in functional analysis over nonarchimedean valued complete fields. Discusses research topics on padic functional analysis and closely related areas.

It offers many features rarely treated in introductory padic texts such as topological models of padic spaces inside euclidian space, a special case of hazewinkels functional equation lemma, and a treatment of analytic elements. A little padic functional analysis part 1 of 2 im going to start with a little bit of terminology and notation about nonarchimedean banach spaces trusting that you can. A functional calculus is a substitution of a bounded operator to a function on. Pdf p adic generalization of the feynman path integrals in quantum mechanics is considered. Pdf summation of padic functional series in integer points. International conference on padic functional analysis 14th. This is a beautiful theory with many arithmetical applications. Application of the p adic analysis and green function in. In the p adic integers, congruences are approximations. Throughout this course k is a finite extension of the field qp of padic numbers.

Discusses research topics on p adic functional analysis and closely related areas. This site is like a library, use search box in the widget to get ebook that you want. The first term, i presented several classical results on zeta functions in characteristic p weils calculation of the zeta. We apply the padic nevanlinna theory to functional equations of the form \g r \circ f\, where r.