Convolution and Equidistribution :: Sato-Tate Theorems for Finite-Field Mellin Transforms.
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new direction...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
2012.
|
| Schriftenreihe: | Annals of mathematics studies ;
no. 180. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a. |
| Beschreibung: | 1 online resource (213 pages) |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781400842704 1400842700 1283379961 9781283379960 |
Internformat
MARC
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| 100 | 1 | |a Katz, Nicholas M. | |
| 245 | 1 | 0 | |a Convolution and Equidistribution : |b Sato-Tate Theorems for Finite-Field Mellin Transforms. |
| 260 | |a Princeton : |b Princeton University Press, |c 2012. | ||
| 300 | |a 1 online resource (213 pages) | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v no. 180 | |
| 588 | 0 | |a Print version record. | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Cover; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. Overview; Chapter 2. Convolution of Perverse Sheaves; Chapter 3. Fibre Functors; Chapter 4. The Situation over a Finite Field; Chapter 5. Frobenius Conjugacy Classes; Chapter 6. Group-Theoretic Facts about Ggeom and Garith; Chapter 7. The Main Theorem; Chapter 8. Isogenies, Connectedness, and Lie-Irreducibility; Chapter 9. Autodualities and Signs; Chapter 10. A First Construction of Autodual Objects; Chapter 11. A Second Construction of Autodual Objects; Chapter 12. The Previous Construction in the Nonsplit Case. | |
| 505 | 8 | |a Chapter 25. G2 Examples: the Overall StrategyChapter 26. G2 Examples: Construction in Characteristic Two; Chapter 27. G2 Examples: Construction in Odd Characteristic; Chapter 28. The Situation over Z: Results; Chapter 29. The Situation over Z: Questions; Chapter 30. Appendix: Deligne's Fibre Functor; Bibliography. | |
| 520 | |a Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a. | ||
| 546 | |a In English. | ||
| 650 | 0 | |a Mellin transform. |0 http://id.loc.gov/authorities/subjects/sh85083428 | |
| 650 | 0 | |a Convolutions (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85031752 | |
| 650 | 0 | |a Sequences (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85120145 | |
| 650 | 6 | |a Transformation de Mellin. | |
| 650 | 6 | |a Convolutions (Mathématiques) | |
| 650 | 6 | |a Suites (Mathématiques) | |
| 650 | 7 | |a MATHEMATICS |x Functional Analysis. |2 bisacsh | |
| 650 | 7 | |a Convolutions (Mathematics) |2 fast | |
| 650 | 7 | |a Mellin transform |2 fast | |
| 650 | 7 | |a Sequences (Mathematics) |2 fast | |
| 655 | 7 | |a dissertations. |2 aat | |
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| 655 | 7 | |a Thèses et écrits académiques. |2 rvmgf | |
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| 776 | 0 | 8 | |i Print version: |a Katz, Nicholas M. |t Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. |d Princeton : Princeton University Press, ©2012 |z 9780691153315 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 180. |0 http://id.loc.gov/authorities/names/n42002129 | |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn769343171 |
|---|---|
| _version_ | 1816881781145600000 |
| adam_text | |
| any_adam_object | |
| author | Katz, Nicholas M. |
| author_facet | Katz, Nicholas M. |
| author_role | |
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| bvnumber | localFWS |
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| callnumber-raw | QA432 .K388 2012 |
| callnumber-search | QA432 .K388 2012 |
| callnumber-sort | QA 3432 K388 42012 |
| callnumber-subject | QA - Mathematics |
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| collection | ZDB-4-EBA |
| contents | Cover; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. Overview; Chapter 2. Convolution of Perverse Sheaves; Chapter 3. Fibre Functors; Chapter 4. The Situation over a Finite Field; Chapter 5. Frobenius Conjugacy Classes; Chapter 6. Group-Theoretic Facts about Ggeom and Garith; Chapter 7. The Main Theorem; Chapter 8. Isogenies, Connectedness, and Lie-Irreducibility; Chapter 9. Autodualities and Signs; Chapter 10. A First Construction of Autodual Objects; Chapter 11. A Second Construction of Autodual Objects; Chapter 12. The Previous Construction in the Nonsplit Case. Chapter 25. G2 Examples: the Overall StrategyChapter 26. G2 Examples: Construction in Characteristic Two; Chapter 27. G2 Examples: Construction in Odd Characteristic; Chapter 28. The Situation over Z: Results; Chapter 29. The Situation over Z: Questions; Chapter 30. Appendix: Deligne's Fibre Functor; Bibliography. |
| ctrlnum | (OCoLC)769343171 |
| dewey-full | 515.723 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.723 |
| dewey-search | 515.723 |
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| discipline | Mathematik |
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| genre_facet | dissertations. Academic theses Academic theses. Thèses et écrits académiques. |
| id | ZDB-4-EBA-ocn769343171 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:10Z |
| institution | BVB |
| isbn | 9781400842704 1400842700 1283379961 9781283379960 |
| language | English |
| oclc_num | 769343171 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (213 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Princeton University Press, |
| record_format | marc |
| series | Annals of mathematics studies ; |
| series2 | Annals of mathematics studies ; |
| spelling | Katz, Nicholas M. Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. Princeton : Princeton University Press, 2012. 1 online resource (213 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Annals of mathematics studies ; no. 180 Print version record. Includes bibliographical references and index. Cover; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. Overview; Chapter 2. Convolution of Perverse Sheaves; Chapter 3. Fibre Functors; Chapter 4. The Situation over a Finite Field; Chapter 5. Frobenius Conjugacy Classes; Chapter 6. Group-Theoretic Facts about Ggeom and Garith; Chapter 7. The Main Theorem; Chapter 8. Isogenies, Connectedness, and Lie-Irreducibility; Chapter 9. Autodualities and Signs; Chapter 10. A First Construction of Autodual Objects; Chapter 11. A Second Construction of Autodual Objects; Chapter 12. The Previous Construction in the Nonsplit Case. Chapter 25. G2 Examples: the Overall StrategyChapter 26. G2 Examples: Construction in Characteristic Two; Chapter 27. G2 Examples: Construction in Odd Characteristic; Chapter 28. The Situation over Z: Results; Chapter 29. The Situation over Z: Questions; Chapter 30. Appendix: Deligne's Fibre Functor; Bibliography. Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a. In English. Mellin transform. http://id.loc.gov/authorities/subjects/sh85083428 Convolutions (Mathematics) http://id.loc.gov/authorities/subjects/sh85031752 Sequences (Mathematics) http://id.loc.gov/authorities/subjects/sh85120145 Transformation de Mellin. Convolutions (Mathématiques) Suites (Mathématiques) MATHEMATICS Functional Analysis. bisacsh Convolutions (Mathematics) fast Mellin transform fast Sequences (Mathematics) fast dissertations. aat Academic theses fast Academic theses. lcgft http://id.loc.gov/authorities/genreForms/gf2014026039 Thèses et écrits académiques. rvmgf has work: Convolution and equidistribution (Text) https://id.oclc.org/worldcat/entity/E39PCFWpf49DthTjX68X4XJHJC https://id.oclc.org/worldcat/ontology/hasWork Print version: Katz, Nicholas M. Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. Princeton : Princeton University Press, ©2012 9780691153315 Annals of mathematics studies ; no. 180. http://id.loc.gov/authorities/names/n42002129 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=421488 Volltext |
| spellingShingle | Katz, Nicholas M. Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. Annals of mathematics studies ; Cover; Title Page; Copyright Page; Table of Contents; Introduction; Chapter 1. Overview; Chapter 2. Convolution of Perverse Sheaves; Chapter 3. Fibre Functors; Chapter 4. The Situation over a Finite Field; Chapter 5. Frobenius Conjugacy Classes; Chapter 6. Group-Theoretic Facts about Ggeom and Garith; Chapter 7. The Main Theorem; Chapter 8. Isogenies, Connectedness, and Lie-Irreducibility; Chapter 9. Autodualities and Signs; Chapter 10. A First Construction of Autodual Objects; Chapter 11. A Second Construction of Autodual Objects; Chapter 12. The Previous Construction in the Nonsplit Case. Chapter 25. G2 Examples: the Overall StrategyChapter 26. G2 Examples: Construction in Characteristic Two; Chapter 27. G2 Examples: Construction in Odd Characteristic; Chapter 28. The Situation over Z: Results; Chapter 29. The Situation over Z: Questions; Chapter 30. Appendix: Deligne's Fibre Functor; Bibliography. Mellin transform. http://id.loc.gov/authorities/subjects/sh85083428 Convolutions (Mathematics) http://id.loc.gov/authorities/subjects/sh85031752 Sequences (Mathematics) http://id.loc.gov/authorities/subjects/sh85120145 Transformation de Mellin. Convolutions (Mathématiques) Suites (Mathématiques) MATHEMATICS Functional Analysis. bisacsh Convolutions (Mathematics) fast Mellin transform fast Sequences (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85083428 http://id.loc.gov/authorities/subjects/sh85031752 http://id.loc.gov/authorities/subjects/sh85120145 http://id.loc.gov/authorities/genreForms/gf2014026039 |
| title | Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. |
| title_auth | Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. |
| title_exact_search | Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. |
| title_full | Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. |
| title_fullStr | Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. |
| title_full_unstemmed | Convolution and Equidistribution : Sato-Tate Theorems for Finite-Field Mellin Transforms. |
| title_short | Convolution and Equidistribution : |
| title_sort | convolution and equidistribution sato tate theorems for finite field mellin transforms |
| title_sub | Sato-Tate Theorems for Finite-Field Mellin Transforms. |
| topic | Mellin transform. http://id.loc.gov/authorities/subjects/sh85083428 Convolutions (Mathematics) http://id.loc.gov/authorities/subjects/sh85031752 Sequences (Mathematics) http://id.loc.gov/authorities/subjects/sh85120145 Transformation de Mellin. Convolutions (Mathématiques) Suites (Mathématiques) MATHEMATICS Functional Analysis. bisacsh Convolutions (Mathematics) fast Mellin transform fast Sequences (Mathematics) fast |
| topic_facet | Mellin transform. Convolutions (Mathematics) Sequences (Mathematics) Transformation de Mellin. Convolutions (Mathématiques) Suites (Mathématiques) MATHEMATICS Functional Analysis. Mellin transform dissertations. Academic theses Academic theses. Thèses et écrits académiques. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=421488 |
| work_keys_str_mv | AT katznicholasm convolutionandequidistributionsatotatetheoremsforfinitefieldmellintransforms |