Lacunary Polynomials Over Finite Fields:
Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notati...
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| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Saint Louis
Elsevier Science
2014
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| Schlagworte: | |
| Online-Zugang: | FAW01 |
| Zusammenfassung: | Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notations, invariants of polynomials, stem polynomials, fully reducible polynomials, and polynomials with a restricted range. The text then takes a look at Problem I and reduction of Problem II to Problem III. Topics include reduction of the marginal case of Problem II to that of Problem III, proposition on power series, proposition on polynomials, and preliminary remarks on polynomial and differential equations.The publication ponders on Problem III and applications. Topics include homogeneous elementary symmetric systems of equations in finite fields; divisibility maximum properties of the gaussian sums and related questions; common representative systems of a finite abelian group with respect to given subgroups; and difference quotient of functions in finite fields. The monograph also reviews certain families of linear mappings in finite fields, appendix on the degenerate solutions of Problem II, a lemma on the greatest common divisor of polynomials with common gap, and two group-theoretical propositions.The text is a dependable reference for mathematicians and researchers interested in the study of reducible lacunary polynomials over finite fields |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 online resource (268 pages) |
| ISBN: | 9781483257839 9780720420500 |
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| 520 | |a Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notations, invariants of polynomials, stem polynomials, fully reducible polynomials, and polynomials with a restricted range. The text then takes a look at Problem I and reduction of Problem II to Problem III. Topics include reduction of the marginal case of Problem II to that of Problem III, proposition on power series, proposition on polynomials, and preliminary remarks on polynomial and differential equations.The publication ponders on Problem III and applications. Topics include homogeneous elementary symmetric systems of equations in finite fields; divisibility maximum properties of the gaussian sums and related questions; common representative systems of a finite abelian group with respect to given subgroups; and difference quotient of functions in finite fields. The monograph also reviews certain families of linear mappings in finite fields, appendix on the degenerate solutions of Problem II, a lemma on the greatest common divisor of polynomials with common gap, and two group-theoretical propositions.The text is a dependable reference for mathematicians and researchers interested in the study of reducible lacunary polynomials over finite fields | ||
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| discipline | Mathematik |
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| spelling | Rédei, L. Verfasser aut Lacunary Polynomials Over Finite Fields Saint Louis Elsevier Science 2014 © 1973 1 online resource (268 pages) txt rdacontent c rdamedia cr rdacarrier Description based on publisher supplied metadata and other sources Lacunary Polynomials Over Finite Fields focuses on reducible lacunary polynomials over finite fields, as well as stem polynomials, differential equations, and gaussian sums. The monograph first tackles preliminaries and formulation of Problems I, II, and III, including some basic concepts and notations, invariants of polynomials, stem polynomials, fully reducible polynomials, and polynomials with a restricted range. The text then takes a look at Problem I and reduction of Problem II to Problem III. Topics include reduction of the marginal case of Problem II to that of Problem III, proposition on power series, proposition on polynomials, and preliminary remarks on polynomial and differential equations.The publication ponders on Problem III and applications. Topics include homogeneous elementary symmetric systems of equations in finite fields; divisibility maximum properties of the gaussian sums and related questions; common representative systems of a finite abelian group with respect to given subgroups; and difference quotient of functions in finite fields. The monograph also reviews certain families of linear mappings in finite fields, appendix on the degenerate solutions of Problem II, a lemma on the greatest common divisor of polynomials with common gap, and two group-theoretical propositions.The text is a dependable reference for mathematicians and researchers interested in the study of reducible lacunary polynomials over finite fields Finite fields (Algebra) Polynomials Power series Galois-Feld (DE-588)4155896-0 gnd rswk-swf Polynom (DE-588)4046711-9 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Polynom (DE-588)4046711-9 s Galois-Feld (DE-588)4155896-0 s 2\p DE-604 Erscheint auch als Druck-Ausgabe Rédei, L . Lacunary Polynomials Over Finite Fields 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rédei, L. Lacunary Polynomials Over Finite Fields Finite fields (Algebra) Polynomials Power series Galois-Feld (DE-588)4155896-0 gnd Polynom (DE-588)4046711-9 gnd |
| subject_GND | (DE-588)4155896-0 (DE-588)4046711-9 (DE-588)4113937-9 |
| title | Lacunary Polynomials Over Finite Fields |
| title_auth | Lacunary Polynomials Over Finite Fields |
| title_exact_search | Lacunary Polynomials Over Finite Fields |
| title_full | Lacunary Polynomials Over Finite Fields |
| title_fullStr | Lacunary Polynomials Over Finite Fields |
| title_full_unstemmed | Lacunary Polynomials Over Finite Fields |
| title_short | Lacunary Polynomials Over Finite Fields |
| title_sort | lacunary polynomials over finite fields |
| topic | Finite fields (Algebra) Polynomials Power series Galois-Feld (DE-588)4155896-0 gnd Polynom (DE-588)4046711-9 gnd |
| topic_facet | Finite fields (Algebra) Polynomials Power series Galois-Feld Polynom Hochschulschrift |
| work_keys_str_mv | AT redeil lacunarypolynomialsoverfinitefields |