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Exposants de Lojasiewicz dans le cas semi-algebrique p-adique

Azzeddine Fekak, Ahmed Srhir (2002)

Annales Polonici Mathematici

We prove the rationality of the Łojasiewicz exponent for p-adic semi-algebraic functions without compactness hypothesis. In the parametric case, we show that the parameter space can be divided into a finite number of semi-algebraic sets on each of which the Łojasiewicz exponent is constant.

Haar wavelets on the Lebesgue spaces of local fields of positive characteristic

Biswaranjan Behera (2014)

Colloquium Mathematicae

We construct the Haar wavelets on a local field K of positive characteristic and show that the Haar wavelet system forms an unconditional basis for L p ( K ) , 1 < p < ∞. We also prove that this system, normalized in L p ( K ) , is a democratic basis of L p ( K ) . This also proves that the Haar system is a greedy basis of L p ( K ) for 1 < p < ∞.

Kloosterman sums for prime powers in P-adic fields

Stanley J. Gurak (2009)

Journal de Théorie des Nombres de Bordeaux

Let K be a field of degree n over Q p , the field of rational p -adic numbers, say with residue degree f , ramification index e and differential exponent d . Let O be the ring of integers of K and P its unique prime ideal. The trace and norm maps for K / Q p are denoted T r and N , respectively. Fix q = p r , a power of a prime p , and let η be a numerical character defined modulo q and of order o ( η ) . The character η extends to the ring of p -adic integers p in the natural way; namely η ( u ) = η ( u ˜ ) , where u ˜ denotes the residue class...

p-adic Dedekind sums.

Kenneth H. Rosen, William M. Snyder (1985)

Journal für die reine und angewandte Mathematik

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