Arithmetic properties of Heilbronn sums
✍ Scribed by W.L. Fouché
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 235 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0022-314X
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📜 SIMILAR VOLUMES
Throughout this paper, we use the following notations: we denote by Z (resp. N) the set of integers (resp. positive integers) and we write l 1 =log N, l 2 =log log N, l 3 =log log log N and e(:)=e 2i?: . If f(n)=O(g(n)), then we write f (n)< <g(n). We denote by |(n) the number of distinct prime fact
We show that S h (a)= p n=1 e(an hp Âp 2 )< <(h, p&1) 11Â16 p 7Â8 , sharpening a result of Yu. ## 2001 Academic Press Let p be a prime, e(x)=e 2?ix , and define the exponential sum S h (a) by S h (a)= : p n=1 e \ an hp p 2 + . For a long time it was an unsolved problem whether S 1 (a)=o( p) unifo