Automorphic Functions and Number Theory
Shimura, Goro.
Automorphic Functions and Number Theory [electronic resource] / by Goro Shimura. - VIII, 72 p. online resource. - Lecture Notes in Mathematics, 54 0075-8434 ; . - Lecture Notes in Mathematics, 54 .
Automorphic functions on the upper half plane, especially modular functions -- Elliptic curves and the fundamental theorems of the classical theory of complex multiplication -- Relation between the points of finite order on an elliptic curve and the modular functions of higher level -- Abelian varieties and siegel modular functions -- The endomorphism-ring of an abelian variety; the field of moduli of an abelian variety with many complex multiplications -- The class-field-theoretical characterization of K’ (?(z)) -- A further method of constructing class fields -- The hasse zeta function of an algebraic curve -- Infinite galois extensions with l-adic representations -- Further generalization and concluding remarks.
9783540358329
10.1007/BFb0071097 doi
Mathematics.
Mathematics, general.
QA1-939
510
Automorphic Functions and Number Theory [electronic resource] / by Goro Shimura. - VIII, 72 p. online resource. - Lecture Notes in Mathematics, 54 0075-8434 ; . - Lecture Notes in Mathematics, 54 .
Automorphic functions on the upper half plane, especially modular functions -- Elliptic curves and the fundamental theorems of the classical theory of complex multiplication -- Relation between the points of finite order on an elliptic curve and the modular functions of higher level -- Abelian varieties and siegel modular functions -- The endomorphism-ring of an abelian variety; the field of moduli of an abelian variety with many complex multiplications -- The class-field-theoretical characterization of K’ (?(z)) -- A further method of constructing class fields -- The hasse zeta function of an algebraic curve -- Infinite galois extensions with l-adic representations -- Further generalization and concluding remarks.
9783540358329
10.1007/BFb0071097 doi
Mathematics.
Mathematics, general.
QA1-939
510