On Differences of Semicubical Powers |
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Authors: | N Watt |
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Institution: | (1) U.A.E. University, Al Ain, United Arab Emirates, AE |
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Abstract: | For X,Y, >0, let and define I
8(X,Y, ) to be the cardinality of the set. In this paper it is shown that, for >0, Y
2/X
3 = O( ), ![Delta](/content/nvp0mxc9actpnhm8/xxlarge916.gif) = O(Y
3/X
3) and X = O (Y
2), one has I
8(X,Y, ) = O(X
2
Y
2 + X
min (X
{3/2}
Y
3, X
{11/2}
Y
{–1}) + X
min ( {1/3}
X
2
Y
3, X
{14/3}
Y
{1/3})), with the implicit constant depending only on . 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. |
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Keywords: | 2000 Mathematics Subject Classification: 11A99 11L07 11M06 |
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