L-function
- Category
- RIEMANN HYPOTHESIS
- Definition
- A broad class of complex functions generalising the zeta function and encoding arithmetic information.
- Math Level
- TECHNICAL
- Index Excerpt
- L-functions
An -function is a complex analytic function built from arithmetic data, usually with structures analogous to the zeta function such as a Dirichlet series, Euler product and functional equation.
The Riemann zeta function is the prototype. The Generalized Riemann Hypothesis concerns analogous zero-location questions for a much broader -function family.
See also: Riemann zeta function, Euler product, functional equation, Generalized Riemann Hypothesis..