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Analytic Methods in Arithmetic Geometry
This volume contains the proceedings of the Arizona Winter School 2016, which was held from March 12-16, 2016, at The University of Arizona, Tucson, AZ. In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provi...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2019.
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| Colección: | Contemporary Mathematics Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 245 | 1 | 0 | |a Analytic Methods in Arithmetic Geometry |
| 260 | |a Providence : |b American Mathematical Society, |c 2019. | ||
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| 490 | 1 | |a Contemporary Mathematics Ser. ; |v v. 740 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Cover -- Title page -- Contents -- Preface -- Primes, elliptic curves and cyclic groups -- 1. Introduction -- 2. Primes -- 3. Elliptic curves: generalities -- 4. Elliptic curves over \Q: group structure -- 5. Elliptic curves over \Q: division fields -- 6. Elliptic curves over \Q: maximal Galois representations -- 7. Elliptic curves over \Q: two-parameter families -- 8. Elliptic curves over \Q: reductions modulo primes -- 9. Cyclicity question: heuristics and upcoming challenges -- 10. Cyclicity question: asymptotic -- 11. Cyclicity question: lower bound -- 12. Cyclicity question: average | |
| 505 | 8 | |a 13. Primality of +1- _{ } -- 14. Anomalous primes -- 15. Global perspectives -- 16. Final remarks -- Acknowledgments -- References -- Growth and expansion in algebraic groups over finite fields -- 1. Introduction -- 2. Elementary tools -- 3. Growth in a solvable group -- 4. Intersections with varieties -- 5. Growth and diameter in \SL₂() -- 6. Further perspectives and open problems -- Acknowledgments -- References -- Lectures on applied ℓ-adic cohomology -- 1. Introduction -- 2. Examples of trace functions -- 3. Trace functions and Galois representations | |
| 505 | 8 | |a 4. Summing trace functions over \Fq -- 5. Quasi-orthogonality relations -- 6. Trace functions over short intervals -- 7. Autocorrelation of trace functions -- the automorphism group of a sheaf -- 8. Trace functions vs. primes -- 9. Bilinear sums of trace functions -- 10. Trace functions vs. modular forms -- 11. The ternary divisor function in arithmetic progressions to large moduli -- 12. The geometric monodromy group and Sato-Tate laws -- 13. Multicorrelation of trace functions -- 14. Advanced completion methods: the -van der Corput method | |
| 505 | 8 | |a 15. Around Zhang's theorem on bounded gaps between primes -- 16. Advanced completions methods: the + shift -- Acknowledgements -- References -- Sato-Tate distributions -- 1. An introduction to Sato-Tate distributions -- 2. Equidistribution, L-functions, and the Sato-Tate conjecture for elliptic curves -- 3. Sato-Tate groups -- 4. Sato-Tate axioms and Galois endomorphism types -- References -- Back Cover | |
| 520 | |a This volume contains the proceedings of the Arizona Winter School 2016, which was held from March 12-16, 2016, at The University of Arizona, Tucson, AZ. In the last decade or so, analytic methods have had great success in answering questions in arithmetic geometry and number theory. The School provided a unique opportunity to introduce graduate students to analytic methods in arithmetic geometry. The book contains four articles. Alina C. Cojocaru's article introduces sieving techniques to study the group structure of points of the reduction of an elliptic curve modulo a rational prime via its. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Arithmetical algebraic geometry. | |
| 650 | 0 | |a Diophantine analysis. | |
| 650 | 6 | |a Géométrie algébrique arithmétique. | |
| 650 | 6 | |a Analyse diophantienne. | |
| 650 | 7 | |a Arithmetical algebraic geometry |2 fast | |
| 650 | 7 | |a Diophantine analysis |2 fast | |
| 700 | 1 | |a Zureick-Brown, David. | |
| 758 | |i has work: |a Analytic Methods in Arithmetic Geometry (Text) |1 https://id.oclc.org/worldcat/entity/E39PD33qCjqQC6CtcMFB37kCPP |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Bucur, Alina. |t Analytic Methods in Arithmetic Geometry. |d Providence : American Mathematical Society, ©2019 |z 9781470437848 |
| 830 | 0 | |a Contemporary Mathematics Ser. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5990826 |z Texto completo |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL5990826 | ||
| 994 | |a 92 |b IZTAP | ||