Mathematical series | Zeta and L-functions | Series expansions

Dirichlet series

In mathematics, a Dirichlet series is any series of the form where s is complex, and is a complex sequence. It is a special case of general Dirichlet series. Dirichlet series play a variety of important roles in analytic number theory. The most usually seen definition of the Riemann zeta function is a Dirichlet series, as are the Dirichlet L-functions. It is conjectured that the Selberg class of series obeys the generalized Riemann hypothesis. The series is named in honor of Peter Gustav Lejeune Dirichlet. (Wikipedia).

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Integral domain | Multiplicative function | Euler product | Dirichlet character | Summation by parts | Radius of convergence | General Dirichlet series | Absolute convergence | Greatest common divisor | Completely multiplicative function | Von Mangoldt function | Sequence | Mellin transform | Selberg class | Peter Gustav Lejeune Dirichlet | Arithmetic function | Generalized Riemann hypothesis | Pointwise | Mellin inversion theorem | Additive function | Mathematics | Prime omega function | Riemann zeta function | Analytic number theory | Liouville function | Prime zeta function | Power series | Möbius function | Ramanujan's sum | Series (mathematics) | Prime number | Zeta function regularization | Dirichlet L-function | Fiber (mathematics) | Logarithmic derivative | Analytic function | Complex number | Dirichlet convolution | Generating function transformation | Jordan's totient function | Perron's formula | Uniform convergence | Generating function | Divisor function