Displaying similar documents to “Doubling measures with different bases”

Raabe’s formula for p -adic gamma and zeta functions

Henri Cohen, Eduardo Friedman (2008)

Annales de l’institut Fourier

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The classical Raabe formula computes a definite integral of the logarithm of Euler’s Γ -function. We compute p -adic integrals of the p -adic log Γ -functions, both Diamond’s and Morita’s, and show that each of these functions is uniquely characterized by its difference equation and p -adic Raabe formula. We also prove a Raabe-type formula for p -adic Hurwitz zeta functions.

Integrable functions for the Bernoulli measures of rank 1

Hamadoun Maïga (2010)

Annales mathématiques Blaise Pascal

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In this paper, following the p -adic integration theory worked out by A. F. Monna and T. A. Springer [, ] and generalized by A. C. M. van Rooij and W. H. Schikhof [, ] for the spaces which are not σ -compacts, we study the class of integrable p -adic functions with respect to Bernoulli measures of rank 1 . Among these measures, we characterize those which are invertible and we give their inverse in the form of series.

The Heisenberg uncertainty relation in harmonic analysis on p -adic numbers field

Cui Minggen, Zhang Yanying (2005)

Annales mathématiques Blaise Pascal

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In this paper, two important geometric concepts–grapical center and width, are introduced in p -adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in p -adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on p -adic numbers field.

Relaxed algorithms for p -adic numbers

Jérémy Berthomieu, Joris van der Hoeven, Grégoire Lecerf (2011)

Journal de Théorie des Nombres de Bordeaux

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Current implementations of p -adic numbers usually rely on so called zealous algorithms, which compute with truncated p -adic expansions at a precision that can be specified by the user. In combination with Newton-Hensel type lifting techniques, zealous algorithms can be made very efficient from an asymptotic point of view. In the similar context of formal power series, another so called lazy technique is also frequently implemented....