# Difference between revisions of "Talk:Riemann zeta function"

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 Definition:  Mathematical function of a complex variable important in number theory for its connection with the distribution of prime numbers. [d] [e]

I removed the word "positive" from the index set for the Eulerian product, as the prime numbers page already defines prime numbers as being positive. I also changed the domain of validity of the series representation to all complex numbers with real part greater than 1. This will make less sense to a general audience, who probably won't understand complex exponents, but they also won't understand "analytic continuation", or "convergence" for that matter. As it seems standard to describe the domain of validity as the largest possible, I chose to change it. However, the definition for all real numbers > 1 does determine the analytic continuation uniquely, so the original description was not wrong.

Perhaps the functional equation, zeros, and special values should be lumped under a single heading, and then other headings could be created to describe things like various representations of the function and important results involving the function (like applications)? Barry R. Smith 21:29, 27 March 2008 (CDT)

## Infinite Series vs. Dirichlet Series

I noticed that before the series definition of the zeta function, the descriptive term "infinite series" was changed to "Dirichlet series". I believe it should be changed back. Dirichlet series are encountered later in a mathematics education than the zeta function, and much later than the special case of $\zeta (2)$ whose value is often given in a first course on infinite series.