Dispersive estimates and absence of embedded eigenvalues
Herbert Koch, Daniel Tataru (2005)
Journées Équations aux dérivées partielles
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In [
Herbert Koch, Daniel Tataru (2005)
Journées Équations aux dérivées partielles
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In [
Florin P. Boca, Radu N. Gologan (2009)
Annales de l’institut Fourier
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Consider the region obtained by removing from the discs of radius , centered at the points of integer coordinates with . We are interested in the distribution of the free path length (exit time) of a point particle, moving from along a linear trajectory of direction , as . For every integer number , we prove the weak convergence of the probability measures associated with the random variables , explicitly computing the limiting distribution. For , respectively , this...
Todd Cochrane, Jeremy Coffelt, Christopher Pinner (2006)
Journal de Théorie des Nombres de Bordeaux
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For a prime and positive integers with , we show that , the number of simultaneous solutions in to , , , satisfies When we obtain a precise asymptotic count on . This leads to the new twisted exponential sum bound for trinomials , and to results on the average size of such sums.
Voronin, V.V. (2000)
Siberian Mathematical Journal
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Manfred G. Madritsch (2012)
Journal de Théorie des Nombres de Bordeaux
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The present paper deals with the summatory function of functions acting on the digits of an -ary expansion. In particular let be a positive integer, then we call
its -ary expansion. We call a function