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Reciprocity laws are pivotal in number theory, explored through roots of unity and complex multiplication of elliptic functions. Goro Shimura's work presents significant generalizations, detailing these laws via abelian varieties, theta functions, and modular functions, including Siegel modular functions. The book also delves into the zeta function of abelian varieties and the emerging field of algebraic relations among periods of abelian integrals. This comprehensive treatment covers topics previously unexplored, making it a vital resource for researchers in the field.
Nákup knihy
Abelian Varieties with Complex Multiplication and Modular Functions, Goro Shimura
- Jazyk
- Rok vydania
- 1997
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- Titul
- Abelian Varieties with Complex Multiplication and Modular Functions
- Podtitul
- (Pms-46)
- Jazyk
- anglicky
- Autori
- Goro Shimura
- Vydavateľ
- Princeton University Press
- Rok vydania
- 1997
- Väzba
- pevná
- Počet strán
- 232
- ISBN10
- 0691016569
- ISBN13
- 9780691016566
- Série
- Štítky
- Veda, Matematika, Geometria, Algebra, Teória čísel
- Anotácia
- Reciprocity laws are pivotal in number theory, explored through roots of unity and complex multiplication of elliptic functions. Goro Shimura's work presents significant generalizations, detailing these laws via abelian varieties, theta functions, and modular functions, including Siegel modular functions. The book also delves into the zeta function of abelian varieties and the emerging field of algebraic relations among periods of abelian integrals. This comprehensive treatment covers topics previously unexplored, making it a vital resource for researchers in the field.