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On a Conjecture of Chalk by Ping Ding is a Mathematics article available to read on EtoBox.
What is On a Conjecture of Chalk about?
Let f # Z[x] with degree k and let p be a prime. By a complete trigonometric sum we mean a sum of the form S(q, f )= q x=1 e q ( f (x)), where q is a positive integer and e q (:)=exp(2?if (x)Âq). Professor Chalk made a conjecture on the upper bound of S(q, f ) when q is a prime power. We prove Chalk's conjecture, in the affirmative, if p is relatively small but 3. When p 3 is relatively large, we give an alternative upper bound which is best possible. For p=2, we also improve previous results. ## 1997 Academic Press Note that the inequality p t k is a trivial consequence of (3). Let r=r( f ) denote the number of distinct roots of the congruence p &t f $(x)#0(mod p) (0 x<p).
Who reads On a Conjecture of Chalk?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Ping Ding
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-314X)
- Published
- 1997
- Language
- EN
- Field
- Mathematics (Physical Sciences)