Titlebook: Arithmetical Investigations; Representation Theor Shai M. J. Haran Book 2008 Springer-Verlag Berlin Heidelberg 2008 Arithmetic geometry.Bet

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0075-8434 (Z.p.), and between its real (and complex) analogue -the orthogonal O.n. (and unitary U.n. )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and be978-3-540-78378-7978-3-540-78379-4Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Authentication and Authorization,e A/.. The important part of the ergodic action of . on the Adele A. is encoded in the action of . on A./.. We then recall the author formula that connects these two philosophies ([Har2], [Harl]), giving the explicit sums in terms of the Fourier transform of the degree log|.|..

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Introduction: Motivations from Geometry,e A/.. The important part of the ergodic action of . on the Adele A. is encoded in the action of . on A./.. We then recall the author formula that connects these two philosophies ([Har2], [Harl]), giving the explicit sums in terms of the Fourier transform of the degree log|.|..

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Book 2008s contain the p-adic integers Z.p. which are the inverse limit of the finite rings Z/p.n.. This gives rise to a tree, and probability measures w on Z.p. correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L.2.(Z.p.,w). The real analogue o

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