Polynomials with special regard to reducibility:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2000
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
77 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008785461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | X, 558 S. |
| ISBN: | 0521662257 |
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Datensatz im Suchindex
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| adam_text | Titel: Polynomials with special regard to reducibility
Autor: Schinzel, Andrzej
Jahr: 2000
Contents Preface Acknowledgments Introduction Notation page ix x 1 8 1 Arbitrary polynomials over an arbitrary field 12 1.1 Liiroth’s theorem 12 1.2 Theorems of Gordan and E. Noether 15 1.3 Ritt’s first theorem 18 1.4 Ritt’s second theorem 24 1.5 Connection between reducibility and decomposability. The case of two variables 52 1.6 Kronecker’s theorems on factorization of polynomials 58 1.7 Connection between reducibility and decomposability. The case of more than two variables 63 1.8 Some auxiliary results 71 1.9 A connection between irreducibility of a polynomial and of its substitution value after a specialization of some of the variables 75 1.10 A polytope and a matrix associated with a polynomial 88 2 Lacunary polynomials over an arbitrary field 92 2.1 Theorems of Capelli and Kneser 92 2.2 Applications to polynomials in many variables 103 2.3 An extension of a theorem of Gourin 110 2.4 Reducibility of polynomials in many variables, that are trinomials with respect to one of them 122 2.5 Reducibility of quadrinomials in many variables 167 2.6 The number of terms of a power of a polynomial 186 v
vi Contents 3 Polynomials over an algebraically closed field 201 3.1 A theorem of E. Noether 201 3.2 Theorems of Ruppert 204 3.3 Salomon’s and Bertini’s theorems on reducibility 215 3.4 The Mahler measure of polynomials over C 222 4 Polynomials over a finitely generated field 263 4.1 A refinement of Gourin’s theorem 263 4.2 A lower bound for the Mahler measure of a polynomial over Z 271 4.3 The greatest common divisor of KP(x ni ,..., x nk ) and KQ(x ni , ...,x nk ) — 277 4.4 Hilbert’s irreducibility theorem 298 5 Polynomials over a number field 315 5.1 Introduction 315 5.2 The classes Ci(K, r, 1) 319 5.3 Families of diagonal ternary quadratic forms each isotropic over K 325 5.4 The class C x (K,r, 2) 331 5.5 The class C; (K, r, 2) for i ^ 1 339 5.6 The class Cq(K, r, s) for arbitrary s 355 5.7 The class C ( K , r, s) for arbitrary s 369 5.8 The class C2(K, r, s) for arbitrary s 375 5.9 A digression on kernels of lacunary polynomials 382 6 Polynomials over a Kroneckerian field 390 6.1 The Mahler measure of non-self-inversive polynomials 390 6.2 Non-self-inversive factors of a lacunary polynomial 420 6.3 Self-inversive factors of lacunary polynomials 435 6.4 The generalized Brauers-Hopf problem 473 Appendices 481 Appendix A. Algebraic functions of one variable 481 Appendix B. Elimination theory 492 Appendix C. Permutation groups and abstract groups 495 Appendix D. Diophantine equations 498 Appendix E. Matrices and lattices 499 Appendix F. Finite fields and congruences 503 Appendix G. Analysis 505 Appendix I. Inequalities 508 Appendix J. Distribution of primes 510 Appendix K. Convexity 512 Appendix by Umberto Zannier. Proof of Conjecture 1 517
Contents vii Bibliography 540 Indices 555 Index of definitions and conjectures 555 Index of theorems 556 Index of terms 557
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| any_adam_object | 1 |
| author | Schinzel, Andrzej 1937-2021 |
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| author_facet | Schinzel, Andrzej 1937-2021 |
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| discipline | Mathematik |
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| id | DE-604.BV012907176 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:38:13Z |
| institution | BVB |
| isbn | 0521662257 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008785461 |
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| owner_facet | DE-739 DE-20 DE-29T DE-11 |
| physical | X, 558 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spellingShingle | Schinzel, Andrzej 1937-2021 Polynomials with special regard to reducibility Encyclopedia of mathematics and its applications Reduzierbarkeit (DE-588)4513769-9 gnd Körper Algebra (DE-588)4308063-7 gnd Polynom (DE-588)4046711-9 gnd |
| subject_GND | (DE-588)4513769-9 (DE-588)4308063-7 (DE-588)4046711-9 |
| title | Polynomials with special regard to reducibility |
| title_auth | Polynomials with special regard to reducibility |
| title_exact_search | Polynomials with special regard to reducibility |
| title_full | Polynomials with special regard to reducibility A. Schinzel |
| title_fullStr | Polynomials with special regard to reducibility A. Schinzel |
| title_full_unstemmed | Polynomials with special regard to reducibility A. Schinzel |
| title_short | Polynomials with special regard to reducibility |
| title_sort | polynomials with special regard to reducibility |
| topic | Reduzierbarkeit (DE-588)4513769-9 gnd Körper Algebra (DE-588)4308063-7 gnd Polynom (DE-588)4046711-9 gnd |
| topic_facet | Reduzierbarkeit Körper Algebra Polynom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008785461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT schinzelandrzej polynomialswithspecialregardtoreducibility |