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A padic local monodromy theorem
"... We prove a local monodromy theorem for padic differential equations on an annulus, answering a question of R. Crew. Specifically, suppose given a finite free module over the Robba ring (the ring of germs of functions analytic on some open padic annulus with outer radius 1) with a connection and a ..."
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Cited by 49 (17 self)
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compatible Frobenius structure. We prove that the module admits a basis over a finite extension of the Robba ring (induced by a finite cover of the open padic unit disc) on which the connection acts via a nilpotent matrix. 1
SEARCHING FOR pADIC EIGENFUNCTIONS
 MATHEMATICAL RESEARCH LETTERS
, 1995
"... In doing padic analysis on spaces of classical modular functions and forms, it is convenient and traditional to broaden the notion of “modular form” to a class called “overconvergent padic modular forms.” Critical for the analysis of the padic Banach spaces composed of this wider class of forms i ..."
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Cited by 6 (0 self)
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is the “Atkin Uoperator”, which is completely continuous and whose spectral theory (still not very well understood) seems to be the key to a good deal of arithmetic. The part of the spectrum of U corresponding to eigenvalues which are padic units 1 is somewhat more understood, thanks to the work of Hida
ON THE ORDER OF VANISHING OF pADIC LFUNCTIONS AT s = 1
, 905
"... Abstract. We review two classical constructions of the cyclotomic padic Lfunction attached to a Hecke cusp form for Γ0(N) and recall some facts about its set of zeros. After that, we firstly prove that for a weight 2 cusp form, its attached MazurTateTeitelbaum padic Lfunction is not identicall ..."
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function is not identically zero over the group of padic units, furthermore, if p is an ordinary prime for the cusp form and a primitive root modulo N, the padic Lfunction is not identically zero modulo p provided that not all the modular integrals vanish modulo p. Secondly, we prove that this padic Lfunction has a non
Uniformly distributed sequences of padic integers
 Math. Appl
, 2002
"... Abstract. The paper describes ergodic (with respect to the Haar measure) functions in the class of all functions that are defined on (and take values in) the ring Zp of padic integers, and satisfy (at least, locally) the Lipschitz condition with coefficient 1. Equiprobable (in particular, measurep ..."
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Cited by 34 (9 self)
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preserving) functions of this class are described also. In some cases (and especially for p = 2) the descriptions are given by explicit formulae. Some of the results may be viewed as descriptions of ergodic isometric dynamical systems on the padic unit disk. The study is motivated by the problem of pseudorandom number
p–Adic pseudodifferential operators and p–adic wavelets
, 2003
"... We introduce a new wide class of p–adic pseudodifferential operators. We show that the basis of p–adic wavelets is the basis of eigenvectors for the introduced operators. 1 ..."
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We introduce a new wide class of p–adic pseudodifferential operators. We show that the basis of p–adic wavelets is the basis of eigenvectors for the introduced operators. 1
p–Adic pseudodifferential operators and p–adic wavelets
, 2003
"... We introduce a new wide class of p–adic pseudodifferential operators. We show that the basis of p–adic wavelets is the basis of eigenvectors for the introduced operators. 1 ..."
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We introduce a new wide class of p–adic pseudodifferential operators. We show that the basis of p–adic wavelets is the basis of eigenvectors for the introduced operators. 1
pAdic Strings and Noncommutativity
 in Noncommutative Structures in Mathematics and Physics
, 2001
"... We consider adelic approach to strings and spatial noncommutativity. Path integral method to string amplitudes is emphasized. Uncertainties in spatial measurements in quantum gravity are related to noncommutativity between coordinates. pAdic and adelic Moyal products are introduced. In particular, ..."
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Cited by 9 (7 self)
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We consider adelic approach to strings and spatial noncommutativity. Path integral method to string amplitudes is emphasized. Uncertainties in spatial measurements in quantum gravity are related to noncommutativity between coordinates. pAdic and adelic Moyal products are introduced. In particular
Results 1  10
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