Euler product

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The infinite product

where is a real number and runs through all prime numbers. This product converges absolutely for all . The analogous product for complex numbers converges absolutely for and defines in this domain the Riemann zeta-function


See also Euler identity and Zeta-function.

How to Cite This Entry:
Euler product. S.A. Stepanov (originator), Encyclopedia of Mathematics. URL:
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098