Character sums with exponential functions and their applications:
The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links between number theory and computer science as well as to other areas of mathematics. Possible applications include (but are not limited to) com...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1999
|
| Schriftenreihe: | Cambridge tracts in mathematics
136 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 UBR01 URL des Erstveröffentlichers |
| Zusammenfassung: | The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links between number theory and computer science as well as to other areas of mathematics. Possible applications include (but are not limited to) complexity theory, random number generation, cryptography, and coding theory. The main method discussed is based on bounds of exponential sums. Accordingly, the book contains many estimates of such sums, including new estimates of classical Gaussian sums. It also contains many open questions and proposals for further research |
| Beschreibung: | 1 Online-Ressource (viii, 163 Seiten) |
| ISBN: | 9780511542930 |
| DOI: | 10.1017/CBO9780511542930 |
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| 505 | 8 | |a pt. 1. Preliminaries -- 1. Introduction -- 2. Notation and Auxiliary Results -- pt. 2. Bounds of Character Sums -- 3. Bounds of Long Character Sums -- 4. Bounds of Short Character Sums -- 5. Bounds of Character Sums for Almost All Moduli -- 6. Bounds of Gaussian Sums -- pt. 3. Multiplicative Translations of Sets -- 7. Multiplicative Translations of Subgroups of F*[subscript p] -- 8. Multiplicative Translations of Arbitrary Sets Modulo p -- pt. 4. Applications to Algebraic Number Fields -- 9. Representatives of Residue Classes -- 10. Cyclotomic Fields and Gaussian Periods -- pt. 5. Applications to Pseudo-Random Number Generators -- 11. Prediction of Pseudo-Random Number Generators -- 12. Congruential Pseudo-Random Number Generators -- pt. 6. Applications to Finite Fields -- 13. Small mth Roots Modulo p -- 14. Supersingular Hyperelliptic Curves -- 15. Distribution of Powers of Primitive Roots -- pt. 7. Applications to Coding Theory and Combinatorics -- 16. Difference Sets in V[subscript p] -- 17. Dimension of BCH Codes -- 18. An Enumeration Problem in Finite Fields | |
| 520 | |a The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links between number theory and computer science as well as to other areas of mathematics. Possible applications include (but are not limited to) complexity theory, random number generation, cryptography, and coding theory. The main method discussed is based on bounds of exponential sums. Accordingly, the book contains many estimates of such sums, including new estimates of classical Gaussian sums. It also contains many open questions and proposals for further research | ||
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Datensatz im Suchindex
| _version_ | 1804176884440760320 |
|---|---|
| any_adam_object | |
| author | Konjagin, Sergej Vladimirovič 1957- |
| author_GND | (DE-588)1116970546 (DE-588)1089271212 |
| author_facet | Konjagin, Sergej Vladimirovič 1957- |
| author_role | aut |
| author_sort | Konjagin, Sergej Vladimirovič 1957- |
| author_variant | s v k sv svk |
| building | Verbundindex |
| bvnumber | BV043942038 |
| classification_rvk | SK 180 |
| collection | ZDB-20-CBO |
| contents | pt. 1. Preliminaries -- 1. Introduction -- 2. Notation and Auxiliary Results -- pt. 2. Bounds of Character Sums -- 3. Bounds of Long Character Sums -- 4. Bounds of Short Character Sums -- 5. Bounds of Character Sums for Almost All Moduli -- 6. Bounds of Gaussian Sums -- pt. 3. Multiplicative Translations of Sets -- 7. Multiplicative Translations of Subgroups of F*[subscript p] -- 8. Multiplicative Translations of Arbitrary Sets Modulo p -- pt. 4. Applications to Algebraic Number Fields -- 9. Representatives of Residue Classes -- 10. Cyclotomic Fields and Gaussian Periods -- pt. 5. Applications to Pseudo-Random Number Generators -- 11. Prediction of Pseudo-Random Number Generators -- 12. Congruential Pseudo-Random Number Generators -- pt. 6. Applications to Finite Fields -- 13. Small mth Roots Modulo p -- 14. Supersingular Hyperelliptic Curves -- 15. Distribution of Powers of Primitive Roots -- pt. 7. Applications to Coding Theory and Combinatorics -- 16. Difference Sets in V[subscript p] -- 17. Dimension of BCH Codes -- 18. An Enumeration Problem in Finite Fields |
| ctrlnum | (ZDB-20-CBO)CR9780511542930 (OCoLC)704481404 (DE-599)BVBBV043942038 |
| dewey-full | 512/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.73 |
| dewey-search | 512/.73 |
| dewey-sort | 3512 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511542930 |
| format | Electronic eBook |
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| id | DE-604.BV043942038 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511542930 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029351008 |
| oclc_num | 704481404 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (viii, 163 Seiten) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO ZDB-20-CBO UBR Einzelkauf (Lückenergänzung CUP Serien 2018) |
| publishDate | 1999 |
| publishDateSearch | 1999 |
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| publisher | Cambridge University Press |
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| spelling | Konjagin, Sergej Vladimirovič 1957- Verfasser (DE-588)1116970546 aut Character sums with exponential functions and their applications Sergei V. Konyagin, Igor E. Shparlinski Character Sums with Exponential Functions & their Applications Cambridge Cambridge University Press 1999 1 Online-Ressource (viii, 163 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 136 pt. 1. Preliminaries -- 1. Introduction -- 2. Notation and Auxiliary Results -- pt. 2. Bounds of Character Sums -- 3. Bounds of Long Character Sums -- 4. Bounds of Short Character Sums -- 5. Bounds of Character Sums for Almost All Moduli -- 6. Bounds of Gaussian Sums -- pt. 3. Multiplicative Translations of Sets -- 7. Multiplicative Translations of Subgroups of F*[subscript p] -- 8. Multiplicative Translations of Arbitrary Sets Modulo p -- pt. 4. Applications to Algebraic Number Fields -- 9. Representatives of Residue Classes -- 10. Cyclotomic Fields and Gaussian Periods -- pt. 5. Applications to Pseudo-Random Number Generators -- 11. Prediction of Pseudo-Random Number Generators -- 12. Congruential Pseudo-Random Number Generators -- pt. 6. Applications to Finite Fields -- 13. Small mth Roots Modulo p -- 14. Supersingular Hyperelliptic Curves -- 15. Distribution of Powers of Primitive Roots -- pt. 7. Applications to Coding Theory and Combinatorics -- 16. Difference Sets in V[subscript p] -- 17. Dimension of BCH Codes -- 18. An Enumeration Problem in Finite Fields The theme of this book is the study of the distribution of integer powers modulo a prime number. It provides numerous new, sometimes quite unexpected, links between number theory and computer science as well as to other areas of mathematics. Possible applications include (but are not limited to) complexity theory, random number generation, cryptography, and coding theory. The main method discussed is based on bounds of exponential sums. Accordingly, the book contains many estimates of such sums, including new estimates of classical Gaussian sums. It also contains many open questions and proposals for further research Exponential sums Modularithmetik (DE-588)4325008-7 gnd rswk-swf Primzahl (DE-588)4047263-2 gnd rswk-swf Potenz Mathematik (DE-588)4175493-1 gnd rswk-swf Natürliche Zahl (DE-588)4041357-3 gnd rswk-swf Natürliche Zahl (DE-588)4041357-3 s Potenz Mathematik (DE-588)4175493-1 s Modularithmetik (DE-588)4325008-7 s Primzahl (DE-588)4047263-2 s DE-604 Shparlinski, Igor E. 20. Jht. Sonstige (DE-588)1089271212 oth Erscheint auch als Druck-Ausgabe 978-0-521-64263-7 https://doi.org/10.1017/CBO9780511542930 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Konjagin, Sergej Vladimirovič 1957- Character sums with exponential functions and their applications pt. 1. Preliminaries -- 1. Introduction -- 2. Notation and Auxiliary Results -- pt. 2. Bounds of Character Sums -- 3. Bounds of Long Character Sums -- 4. Bounds of Short Character Sums -- 5. Bounds of Character Sums for Almost All Moduli -- 6. Bounds of Gaussian Sums -- pt. 3. Multiplicative Translations of Sets -- 7. Multiplicative Translations of Subgroups of F*[subscript p] -- 8. Multiplicative Translations of Arbitrary Sets Modulo p -- pt. 4. Applications to Algebraic Number Fields -- 9. Representatives of Residue Classes -- 10. Cyclotomic Fields and Gaussian Periods -- pt. 5. Applications to Pseudo-Random Number Generators -- 11. Prediction of Pseudo-Random Number Generators -- 12. Congruential Pseudo-Random Number Generators -- pt. 6. Applications to Finite Fields -- 13. Small mth Roots Modulo p -- 14. Supersingular Hyperelliptic Curves -- 15. Distribution of Powers of Primitive Roots -- pt. 7. Applications to Coding Theory and Combinatorics -- 16. Difference Sets in V[subscript p] -- 17. Dimension of BCH Codes -- 18. An Enumeration Problem in Finite Fields Exponential sums Modularithmetik (DE-588)4325008-7 gnd Primzahl (DE-588)4047263-2 gnd Potenz Mathematik (DE-588)4175493-1 gnd Natürliche Zahl (DE-588)4041357-3 gnd |
| subject_GND | (DE-588)4325008-7 (DE-588)4047263-2 (DE-588)4175493-1 (DE-588)4041357-3 |
| title | Character sums with exponential functions and their applications |
| title_alt | Character Sums with Exponential Functions & their Applications |
| title_auth | Character sums with exponential functions and their applications |
| title_exact_search | Character sums with exponential functions and their applications |
| title_full | Character sums with exponential functions and their applications Sergei V. Konyagin, Igor E. Shparlinski |
| title_fullStr | Character sums with exponential functions and their applications Sergei V. Konyagin, Igor E. Shparlinski |
| title_full_unstemmed | Character sums with exponential functions and their applications Sergei V. Konyagin, Igor E. Shparlinski |
| title_short | Character sums with exponential functions and their applications |
| title_sort | character sums with exponential functions and their applications |
| topic | Exponential sums Modularithmetik (DE-588)4325008-7 gnd Primzahl (DE-588)4047263-2 gnd Potenz Mathematik (DE-588)4175493-1 gnd Natürliche Zahl (DE-588)4041357-3 gnd |
| topic_facet | Exponential sums Modularithmetik Primzahl Potenz Mathematik Natürliche Zahl |
| url | https://doi.org/10.1017/CBO9780511542930 |
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