Matches in SemOpenAlex for { <https://semopenalex.org/work/W2074558466> ?p ?o ?g. }
Showing items 1 to 68 of
68
with 100 items per page.
- W2074558466 endingPage "929" @default.
- W2074558466 startingPage "912" @default.
- W2074558466 abstract "In this paper we study the maximum–minimum value of polynomials over the integer ring Z . In particular, we prove the following: Let F ( x , y ) be a polynomial over Z . Then, max x ∈ Z ( T ) min y ∈ Z | F ( x , y ) | = o ( T 1 / 2 ) as T → ∞ if and only if there is a positive integer B such that max x ∈ Z min y ∈ Z | F ( x , y ) | ⩽ B . We then apply these results to exponential diophantine equations and obtain that: Let f ( x , y ) , g ( x , y ) and G ( x , y ) be polynomials over Q , G ( x , y ) ∈ ( Q [ x , y ] − Q [ x ] ) ∪ Q , and b a positive integer. For every α in Z , there is a y in Z such that f ( α , y ) + g ( α , y ) b G ( α , y ) = 0 if and only if for every integer α there exists an h ( x ) ∈ Q [ x ] such that f ( x , h ( x ) ) + g ( x , h ( x ) ) b G ( x , h ( x ) ) ≡ 0 , and h ( α ) ∈ Z ." @default.
- W2074558466 created "2016-06-24" @default.
- W2074558466 creator A5033429649 @default.
- W2074558466 date "2010-04-01" @default.
- W2074558466 modified "2023-09-26" @default.
- W2074558466 title "Max–min of polynomials and exponential diophantine equations" @default.
- W2074558466 cites W1732310309 @default.
- W2074558466 cites W2001331304 @default.
- W2074558466 cites W2010073966 @default.
- W2074558466 cites W2012827373 @default.
- W2074558466 cites W2042877335 @default.
- W2074558466 cites W2077295563 @default.
- W2074558466 cites W4238395816 @default.
- W2074558466 doi "https://doi.org/10.1016/j.jnt.2009.11.006" @default.
- W2074558466 hasPublicationYear "2010" @default.
- W2074558466 type Work @default.
- W2074558466 sameAs 2074558466 @default.
- W2074558466 citedByCount "1" @default.
- W2074558466 countsByYear W20745584662015 @default.
- W2074558466 crossrefType "journal-article" @default.
- W2074558466 hasAuthorship W2074558466A5033429649 @default.
- W2074558466 hasConcept C114614502 @default.
- W2074558466 hasConcept C118615104 @default.
- W2074558466 hasConcept C134306372 @default.
- W2074558466 hasConcept C151376022 @default.
- W2074558466 hasConcept C178790620 @default.
- W2074558466 hasConcept C185592680 @default.
- W2074558466 hasConcept C199360897 @default.
- W2074558466 hasConcept C206530611 @default.
- W2074558466 hasConcept C2780378348 @default.
- W2074558466 hasConcept C33923547 @default.
- W2074558466 hasConcept C41008148 @default.
- W2074558466 hasConcept C90119067 @default.
- W2074558466 hasConcept C97137487 @default.
- W2074558466 hasConceptScore W2074558466C114614502 @default.
- W2074558466 hasConceptScore W2074558466C118615104 @default.
- W2074558466 hasConceptScore W2074558466C134306372 @default.
- W2074558466 hasConceptScore W2074558466C151376022 @default.
- W2074558466 hasConceptScore W2074558466C178790620 @default.
- W2074558466 hasConceptScore W2074558466C185592680 @default.
- W2074558466 hasConceptScore W2074558466C199360897 @default.
- W2074558466 hasConceptScore W2074558466C206530611 @default.
- W2074558466 hasConceptScore W2074558466C2780378348 @default.
- W2074558466 hasConceptScore W2074558466C33923547 @default.
- W2074558466 hasConceptScore W2074558466C41008148 @default.
- W2074558466 hasConceptScore W2074558466C90119067 @default.
- W2074558466 hasConceptScore W2074558466C97137487 @default.
- W2074558466 hasIssue "4" @default.
- W2074558466 hasLocation W20745584661 @default.
- W2074558466 hasOpenAccess W2074558466 @default.
- W2074558466 hasPrimaryLocation W20745584661 @default.
- W2074558466 hasRelatedWork W1922638020 @default.
- W2074558466 hasRelatedWork W1975709759 @default.
- W2074558466 hasRelatedWork W2023338413 @default.
- W2074558466 hasRelatedWork W2138312577 @default.
- W2074558466 hasRelatedWork W2139984395 @default.
- W2074558466 hasRelatedWork W2321787319 @default.
- W2074558466 hasRelatedWork W2325635326 @default.
- W2074558466 hasRelatedWork W2354387820 @default.
- W2074558466 hasRelatedWork W2356648190 @default.
- W2074558466 hasRelatedWork W3174056594 @default.
- W2074558466 hasVolume "130" @default.
- W2074558466 isParatext "false" @default.
- W2074558466 isRetracted "false" @default.
- W2074558466 magId "2074558466" @default.
- W2074558466 workType "article" @default.