Matches in SemOpenAlex for { <https://semopenalex.org/work/W2696583186> ?p ?o ?g. }
Showing items 1 to 71 of
71
with 100 items per page.
- W2696583186 endingPage "774" @default.
- W2696583186 startingPage "757" @default.
- W2696583186 abstract "where p is a prime power , χ mod p is a Dirichlet character, a, b, n are integers with n ≥ 2. The first sum was studied in connection with Waring’s problem and we have a classical result due to professor Hua [10]. The second sum has not been studied before as far as the authors know. We hope it can be used in the work of generalizing Waring’s problem. In [6], Davenport and Heilbronn showed that (1.3) S(ax + bx, p) n p(b, p), if p a, where θ = 2/3 if n = 3, and θ = 3/4 if n ≥ 3. Hua [10] showed that θ = 1/2 for all n ≥ 2 (also see Lemma 4.1 of Vaughan [19]). Hua’s proof depends on Weil’s estimate for exponential sums over finite fields (see Bombieri [1] or Schmidt [15]). In this case we have (1.4) |S(ax + bx, p)| ≤ (n− 1)p 2 , if p a. For m ≥ 2, following the work of Loxton and Smith [13], and Smith [17], one has that (1.5) |S(ax + bx, p)| ≤ dn−1(p)p m 2 (∆, p) 1 2 , where dn−1(p) is the number of representations of p as a product of n−1 positive integers and ∆ is the discriminant of the derivative of the polynomial ax+bx. After an improvement by Loxton and Vaughan, Theorem 1 of [14] implies the following estimate (1.6) |S(ax + bx, p)| ≤ (n− 1)p m+τ0 2 (D, p) 1 2 , where D is the different of the derivative of the polynomial ax + bx, and τ0 = 1 if p ≤ n, and τ0 = 0 if p > n. Very recently, Dabrowski and Fisher established better bounds for exponential sums of this kind. Under the restriction p ab, p n, and" @default.
- W2696583186 created "2017-06-30" @default.
- W2696583186 creator A5000582109 @default.
- W2696583186 creator A5001319677 @default.
- W2696583186 date "2000-01-01" @default.
- W2696583186 modified "2023-10-18" @default.
- W2696583186 title "Bounds for certain exponential sums" @default.
- W2696583186 cites W1661423033 @default.
- W2696583186 cites W1933741972 @default.
- W2696583186 cites W2002760437 @default.
- W2696583186 cites W2036595899 @default.
- W2696583186 cites W2040594718 @default.
- W2696583186 cites W2041479497 @default.
- W2696583186 cites W2059946380 @default.
- W2696583186 cites W2081163625 @default.
- W2696583186 cites W2104428487 @default.
- W2696583186 cites W2132248880 @default.
- W2696583186 cites W2157499316 @default.
- W2696583186 cites W232197060 @default.
- W2696583186 cites W2334612034 @default.
- W2696583186 cites W249233303 @default.
- W2696583186 cites W2798742957 @default.
- W2696583186 doi "https://doi.org/10.4310/ajm.2000.v4.n4.a3" @default.
- W2696583186 hasPublicationYear "2000" @default.
- W2696583186 type Work @default.
- W2696583186 sameAs 2696583186 @default.
- W2696583186 citedByCount "22" @default.
- W2696583186 countsByYear W26965831862013 @default.
- W2696583186 countsByYear W26965831862014 @default.
- W2696583186 countsByYear W26965831862016 @default.
- W2696583186 countsByYear W26965831862017 @default.
- W2696583186 countsByYear W26965831862019 @default.
- W2696583186 countsByYear W26965831862022 @default.
- W2696583186 crossrefType "journal-article" @default.
- W2696583186 hasAuthorship W2696583186A5000582109 @default.
- W2696583186 hasAuthorship W2696583186A5001319677 @default.
- W2696583186 hasBestOaLocation W26965831861 @default.
- W2696583186 hasConcept C134306372 @default.
- W2696583186 hasConcept C151376022 @default.
- W2696583186 hasConcept C202444582 @default.
- W2696583186 hasConcept C33923547 @default.
- W2696583186 hasConcept C49016629 @default.
- W2696583186 hasConcept C92867014 @default.
- W2696583186 hasConceptScore W2696583186C134306372 @default.
- W2696583186 hasConceptScore W2696583186C151376022 @default.
- W2696583186 hasConceptScore W2696583186C202444582 @default.
- W2696583186 hasConceptScore W2696583186C33923547 @default.
- W2696583186 hasConceptScore W2696583186C49016629 @default.
- W2696583186 hasConceptScore W2696583186C92867014 @default.
- W2696583186 hasIssue "4" @default.
- W2696583186 hasLocation W26965831861 @default.
- W2696583186 hasLocation W26965831862 @default.
- W2696583186 hasOpenAccess W2696583186 @default.
- W2696583186 hasPrimaryLocation W26965831861 @default.
- W2696583186 hasRelatedWork W1557945163 @default.
- W2696583186 hasRelatedWork W1985218657 @default.
- W2696583186 hasRelatedWork W2096753949 @default.
- W2696583186 hasRelatedWork W2314643997 @default.
- W2696583186 hasRelatedWork W2349513171 @default.
- W2696583186 hasRelatedWork W3106133691 @default.
- W2696583186 hasRelatedWork W3108795105 @default.
- W2696583186 hasRelatedWork W3217624969 @default.
- W2696583186 hasRelatedWork W4249580765 @default.
- W2696583186 hasRelatedWork W4313321100 @default.
- W2696583186 hasVolume "4" @default.
- W2696583186 isParatext "false" @default.
- W2696583186 isRetracted "false" @default.
- W2696583186 magId "2696583186" @default.
- W2696583186 workType "article" @default.