Titlebook: Explorations in Complex Functions; Richard Beals,Roderick S. C. Wong Textbook 2020 Springer Nature Switzerland AG 2020 Complex analysis te

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https://doi.org/10.1007/978-1-4899-0562-8This chapter relies heavily on Chapter ., with some reference to analytic continuation and conformal mapping, particularly Theorem ..

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商议

Riemann surfaces and algebraic curves,A Riemann surface can be thought as the domain of definition of a holomorphic function . that has been continued analytically as far as such continuations can be carried out. In general this is not a domain in the previous sense, i.e. a subset of the plane. Rather it is a complex manifold of one (complex) dimension that projects locally into ..

mechanism

Entire functions,An entire function, a function that is defined and holomorphic in the entire plane ., can be analyzed in terms of its zeros and of its growth. Such an analysis has important applications.

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The Riemann zeta function,As Euler noted, the fact that the series (.) diverges at . gives another proof that the set of primes is infinite—in fact . diverges. (This is only the simplest of the connections between properties of the zeta function and properties of primes.)

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