On Differences of Semicubical Powers

Autor: Nigel Watt
Rok vydání: 2004
Předmět:
Zdroj: Monatshefte f�r Mathematik. 141:45-81
ISSN: 1436-5081
0026-9255
DOI: 10.1007/s00605-003-0049-y
Popis: For X,Y,Δ>0, let and define I8(X,Y,Δ) to be the cardinality of the set. In this paper it is shown that, for e>0, Y2/X3 = O(Δ), Δ = O(Y3/X3) and X = O (Y2), one has I8(X,Y,Δ) = O(X2Y2 + Xe min (X{3/2}Y3, Δ X{11/2}Y{−1}) + Xe min (Δ{1/3}X2Y3, Δ X{14/3}Y{1/3})), with the implicit constant depending only on e. There is a brief report on an application of this that leads, by way of the Bombieri-Iwaniec method for exponential sums, to some improvement of results on the mean squared modulus of a Dirichlet L-function along a ‘short’ interval of its critical line.
Databáze: OpenAIRE
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