Equations over finite fields: an elementary approach
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1976
|
| Series: | Lecture notes in mathematics
536 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 267 S. |
| ISBN: | 354007855X 038707855X |
Staff View
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| 245 | 1 | 0 | |a Equations over finite fields |b an elementary approach |c Wolfgang M. Schmidt |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1976 | |
| 300 | |a IX, 267 S. | ||
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| 490 | 1 | |a Lecture notes in mathematics |v 536 | |
| 650 | 4 | |a Analyse diophantienne | |
| 650 | 4 | |a Champs modulaires | |
| 650 | 4 | |a Diophantine analysis | |
| 650 | 4 | |a Finite fields (Algebra) | |
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Chapter Page
Introduction 1
I. Equations yd = f(x) and yq - y = f(x)
1. Finite Fields 3
2. Equations y = f (x) 8
3. Construction of certain polynomials 16
4. Proof of the Main Theorem 21
5. Removal of the condition (m,d) =1 22
6. Hyperderivatives 27
2
7. Removal of the condition that q = p or p .... 31
8. The Work of Stark. . 32
9. Equations yq - y = f(x) 34
II. Character Suras and Exponential Sums
1. Characters of Finite Abelian Groups 38
2. Characters and Character Sums associated with
Finite Fields 41
3. Gaussian Sums 46
4. The low road 50
5. Systems of equations y 1 = f (x),...,y n =
Vx) 52
6. Auxiliary lemmas on »}*+... + (O^ 57
7. Further auxiliary lemmas 60
8. Zeta Function and L-Functions 62
9. Special L-Functions 65
10. Field extensions. The Davenport - Hasse relations . 72
11. Proof of the Principal Theorems 77
VIII
Chapter Page
12. Kloosterman Sums 84
13. Further Results 88
III. Absolutely Irreducible Equations f(x,y) = 0
1. Introduction 92
2. Independence results 97
3. Derivatives 105
4. Construction of two algebraic functions 107
5. Construction of two polynomials 114
6. Proof of the Main Theorem 116
7. Valuations 119
8. Hyperderivatives again 125
9. Removal of the condition that q = P 131
IV. Equations in Many Variables
1. Theorems of Chevalley and Warning 134
2. Quadratic forms 140
3. Elementary upper bounds. Projective zeros 147
4. The average number of zeros of a polynomial. . . . 157
5. Additive Equations: A Chebychev Argument 160
6. Additive Equations: Character Sums 166
7. Equations f1(y)x1 1l+.. .+fn(y)xndn = 0 173
V. Absolutely Irreducible Equations f(x , ...,x ) = 0
1. Elimination Theory 177
2. The absolute irreducibility of polynomials (I) . . 190
3. The absolute irreducibility of polynomials (II). . 194
4. The absolute irreducibility of polynomials (III) . 204
IX
Chapter Page
5. The number of zeros of absolutely irreducible
polynomials in n variables 210
VI. Rudiments of Algebraic Geometry. The Number of Points
in Varieties over Finite Fields
1. Varieties 216
2. Dimension 228
3. Rational Maps 235
4. Birational Maps 244
5. Linear Disjointness of Fields 250
6. Constant Field Extensions 254
7. Counting Points in Varieties Over Finite Fields. . 260
BIBLIOGRAPHY 265
|
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| dewey-search | 512.9/4 510/.8 |
| dewey-sort | 3512.9 14 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV002243133 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:39Z |
| institution | BVB |
| isbn | 354007855X 038707855X |
| language | English |
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| oclc_num | 721423640 |
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| physical | IX, 267 S. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
| publishDateSort | 1976 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Schmidt, Wolfgang M. 1933- Verfasser (DE-588)136169627 aut Equations over finite fields an elementary approach Wolfgang M. Schmidt Berlin [u.a.] Springer 1976 IX, 267 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 536 Analyse diophantienne Champs modulaires Diophantine analysis Finite fields (Algebra) Diophantische Gleichung (DE-588)4012386-8 gnd rswk-swf Diophantische Gleichung (DE-588)4012386-8 s DE-604 Lecture notes in mathematics 536 (DE-604)BV000676446 536 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001474185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schmidt, Wolfgang M. 1933- Equations over finite fields an elementary approach Lecture notes in mathematics Analyse diophantienne Champs modulaires Diophantine analysis Finite fields (Algebra) Diophantische Gleichung (DE-588)4012386-8 gnd |
| subject_GND | (DE-588)4012386-8 |
| title | Equations over finite fields an elementary approach |
| title_auth | Equations over finite fields an elementary approach |
| title_exact_search | Equations over finite fields an elementary approach |
| title_full | Equations over finite fields an elementary approach Wolfgang M. Schmidt |
| title_fullStr | Equations over finite fields an elementary approach Wolfgang M. Schmidt |
| title_full_unstemmed | Equations over finite fields an elementary approach Wolfgang M. Schmidt |
| title_short | Equations over finite fields |
| title_sort | equations over finite fields an elementary approach |
| title_sub | an elementary approach |
| topic | Analyse diophantienne Champs modulaires Diophantine analysis Finite fields (Algebra) Diophantische Gleichung (DE-588)4012386-8 gnd |
| topic_facet | Analyse diophantienne Champs modulaires Diophantine analysis Finite fields (Algebra) Diophantische Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001474185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT schmidtwolfgangm equationsoverfinitefieldsanelementaryapproach |