nLab analytic continuation

1. Idea

In analysis, analytic continuation refers to the extension of the domain of an analytic function.

In particular it often refers to the extension of an analytic function on the real line to a holomorphic function on the complex plane.

2. Related concepts

• analytically continued Chern-Simons theory

• zeta function

• zeta function regularization

• Wick rotation, thermal quantum field theory

3. References

See also

• Wikipedia, Analytic continuation

In p-adic geometry the need for analytic continuation motivates the G-topology, see the introduction of

• Siegfried Bosch, Ulrich Güntzer, Reinhold Remmert, Non-Archimedean Analysis – A systematic approach to rigid analytic geometry, 1984 (pdf)