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The distribution of exponential sums

  • J. H. Loxton (a1)


We shall consider incomplete exponential sums of the shape

where q, a and h are integers satisfying 1 ≤ a < a + h ≤ q, f(x) is a function denned at least for the integers in the range of summation, and eq(t) is an abbreviation for e2πit/q.



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1.Feller, W.. An introduction to probability theory and its applications, Volume 2 (Wiley, 1966).
2.Hooley, C.. On the greatest prime factor of a cubic polynomial. J. reine angew. Math., 303/304 (1978), 2150.
3.Lehmer, D. H.. Incomplete Gauss sums. Mathematika, 23 (1976), 125135.
4.Loxton, J. H.. The graphs of exponential sums. Mathematika, 30 (1983), 153163.
5.Watson, G. N.. A treatise on the theory of Besselfunctions (Cambridge University Press, 1948).
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