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Number Theory Related to Modular Curves : Momose Memorial Volume.
This volume contains the proceedings of the Barcelona-Boston-Tokyo Number Theory Seminar, which was held in memory of Fumiyuki Momose, a distinguished number theorist from Chuo University in Tokyo. Momose, who was a student of Yasutaka Ihara, made important contributions to the theory of Galois repr...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2018.
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| Colección: | Contemporary Mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Contents; Preface; The Barcelona Conference; My friend, Fumiyuki Momose; An overview of the mathematical work of Fumiyuki Momose; 1. Introduction; 2. â#x84;#x93;-adic representations; 3. Rational Points; 4. Cryptography; 5. Concluding Remarks; 6. Publications of Momose; References; A note on algebraic points on Shimura curves; 1. Points on Shimura curves; 2. Automorphism groups and elliptic points; 3. Examples; 4. Estimate of \cNnâ#x82;#x81;(); References; On quadratic points of classical modular curves; 1. Introduction.
- 2. The set of quadratic points is a not finite set: Hyperelliptic and Bielliptic curves3. Automorphism group of classical modular curves; 4. Which curves â#x82;#x80;() have an infinite set of quadratic points?; 5. Other classical modular curves; Acknowledgements; References; -adic point counting on singular superelliptic curves; 1. Introduction; 2. Review of -adic theory; 3. The cohomology of a superelliptic curve; 4. The Matrix of Frobenius; 5. The Algorithm; References; A refinement of a conjecture of Gross, Kohnen, and Zagier; 1. Introduction; 2. Heegner objects.
- 3. On the real locus of â#x82;#x80;â#x81;ð()4. Motivation and evidence; Acknowledgements; References; A vanishing criterion for Dirichlet series with periodic coefficients; 1. Introduction; 2. Preliminaries; 3. Odd functions; 4. Even functions; 5. Conclusion; Acknowledgments; References; Rational families of 17-torsion points of elliptic curves over number fields; 1. Introduction; 2. Rational -torsion over fields of degree; 3. Brillâ#x80;#x93;Noether Varieties; 4. Fine Siegel units and fine Siegel points; 5. Digression: 13-torsion; 6. Families of 17-torsion; 7. Appendix: Gonality; References.
- An explicit integral representation of Siegel-Whittaker functions on (2,â#x84;#x9D;) for the large discrete series representations1. Introduction; 2. Preliminaries; 3. Miyazakiâ#x80;#x99;s results; 4. Partially Confluent hypergeometric functions in two variables; 5. Main results; 6. Proof of main results; 7. Remarks on { _{ }}; References; On implementation of GHS attack against elliptic curve cryptosystems over cubic extension fields of odd characteristic; 1. Introduction; 2. Weak Covering over â#x82;#x83;, char â#x89; 2; 3. How to construct / from â#x82;#x80;/ _{ }
- 4. Transfer DLP from â#x82;#x80;/ â#x82;#x83; to /5. Computer experiments; 6. Conclusion; References; Appendix: On Condition (2.14) of hyperellipticity; The Sato-Tate conjecture for a Picard curve with complex multiplication (with an appendix by Francesc Fité); 1. Introduction; 2. The Sato-Tate group (); 3. Sato-Tate distribution; 4. The moment sequences; References; Appendix (by Francesc Fité); References; Arithmetic twists and Abelian extensions; 1. Introduction; 2. Abelian varieties of type \T; 3. The arithmetic twisting group; 4. A general construction; 5. The ideal _{ }(/).