## Topics in Complex Function Theory, Volume 3: Abelian Functions and Modular Functions of Several VariablesDevelops the higher parts of function theory in a unified presentation. Starts with elliptic integrals and functions and uniformization theory, continues with automorphic functions and the theory of abelian integrals and ends with the theory of abelian functions and modular functions in several variables. The last topic originates with the author and appears here for the first time in book form. |

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Abelian functions According addition algebraic Amer apply arbitrary assume automorphic belongs bounded called Chapter coefficients columns compact complex condition consider constant contained convergence coordinates corresponding defined denote depend derive determined divisor domains elements entire equation equivalent exists expressed factor field finitely fixed follows formula fundamental Furthermore given hand Hence holds homogeneous identically implies independent inequality integral intersection introduce Jacobian functions linear mapping Math matrix means meromorphic modular forms modular functions modular substitution multiplication neighborhood obtain pairs particular period polynomial positive power series proof proved quotient rational region regular function relation relatively prime remains replace respect result rows satisfied solution space sufficiently suitable symmetric symmetric matrix Theorem theory transformation uniquely unit vanish variables varieties vector Volume yields zero

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Page 233 - The volume of the fundamental domain for some infinite groups, Trans. Amer. Math. Soc.

Page 237 - On the Riemann hypothesis in function- fields, Proc. Nat. Acad. Sci. USA 27 (1941), 345-347.