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Abelian Varieties with Complex Multiplication and Modular Functions

(Pms-46)

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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.

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Abelian Varieties with Complex Multiplication and Modular Functions, Goro Shimura

Sprache
Erscheinungsdatum
1997
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(Hardcover)
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Titel
Abelian Varieties with Complex Multiplication and Modular Functions
Untertitel
(Pms-46)
Sprache
Englisch
Autor*innen
Goro Shimura
Erscheinungsdatum
1997
Einband
Hardcover
Seitenzahl
232
ISBN10
0691016569
ISBN13
9780691016566
Reihe
Beschreibung
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.