Displaying similar documents to “The summatory function of q -additive functions on pseudo-polynomial sequences”

A system of simultaneous congruences arising from trinomial exponential sums

Todd Cochrane, Jeremy Coffelt, Christopher Pinner (2006)

Journal de Théorie des Nombres de Bordeaux

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For a prime p and positive integers < k < h < p with d = ( h , k , , p - 1 ) , we show that M , the number of simultaneous solutions x , y , z , w in p * to x h + y h = z h + w h , x k + y k = z k + w k , x + y = z + w , satisfies M 3 d 2 ( p - 1 ) 2 + 25 h k ( p - 1 ) . When h k = o ( p d 2 ) we obtain a precise asymptotic count on M . This leads to the new twisted exponential sum bound x = 1 p - 1 χ ( x ) e 2 π i f ( x ) / p 3 1 4 d 1 2 p 7 8 + 5 h k 1 4 p 5 8 , for trinomials f = a x h + b x k + c x , and to results on the average size of such sums.

Some results on the product of distributions and the change of variable

Emin Özçag, Brian Fisher (1991)

Commentationes Mathematicae Universitatis Carolinae

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Let F and G be distributions in 𝒟 ' and let f be an infinitely differentiable function with f ' ( x ) > 0 , (or < 0 ). It is proved that if the neutrix product F G exists and equals H , then the neutrix product F ( f ) G ( f ) exists and equals H ( f ) .

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let D be a nonempty compact subset of a Banach space X and denote by S ( X ) the family of all nonempty bounded closed convex subsets of X . We endow S ( X ) with the Hausdorff metric and show that there exists a set S ( X ) such that its complement S ( X ) is σ -porous and such that for each A and each x ˜ D , the set of solutions of the best approximation problem x ˜ - z min , z A , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

On the linear independence of p -adic L -functions modulo p

Bruno Anglès, Gabriele Ranieri (2010)

Annales de l’institut Fourier

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Let p 3 be a prime. Let n such that n 1 , let χ 1 , ... , χ n be characters of conductor d not divided by p and let ω be the Teichmüller character. For all i between 1 and n , for all j between 0 and ( p - 3 ) / 2 , set θ i , j = χ i ω 2 j + 1 if χ i is odd ; χ i ω 2 j if χ i is even . Let K = p ( χ 1 , ... , χ n ) and let π be a prime of the valuation ring 𝒪 K of K . For all i , j let f ( T , θ i , j ) be the Iwasawa series associated to θ i , j and f ( T , θ i , j ) ¯ its reduction modulo ( π ) . Finally let 𝔽 p ¯ be an algebraic closure of 𝔽 p . Our main result is that if the characters χ i are all distinct modulo ( π ) , then 1 and the series...