# Dirichlet series/Related Articles

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*See also changes related to Dirichlet series, or pages that link to Dirichlet series or to this page or whose text contains "Dirichlet series".*

## Parent topics

- Number theory [r]: The study of integers and relations between them.
^{[e]} - Series (mathematics) [r]: A sequence of numbers defined by the partial sums of another infinite sequence.
^{[e]} - Arithmetic function [r]: A function defined on the set of positive integers, usually with integer, real or complex values, studied in number theory.
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## Subtopics

- Riemann zeta function [r]: Mathematical function of a complex variable important in number theory for its connection with the distribution of prime numbers.
^{[e]} - Dedekind zeta function [r]: Generalization of the Riemann zeta function to algebraic number fields.
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- Fourier series [r]: Infinite series whose terms are constants multiplied by sine and cosine functions and that can approximate a wide variety of periodic functions.
^{[e]} - Power series [r]: An infinite series whose terms involve successive powers of a variable, typically with real or complex coefficients.
^{[e]} - Puiseaux series [r]:
*Add brief definition or description* - Dirichlet character [r]: A group homomorphism on the multiplicative group in modular arithmetic extended to a multiplicative function on the positive integers.
^{[e]} - Peter Lejeune Dirichlet [r]:
*Add brief definition or description* - Wiener-Ikehara theorem [r]: A Tauberian theorem used in number theory to relate the behaviour of a real sequence to the analytic properties of the associated Dirichlet series.
^{[e]} - Möbius function [r]: Arithmetic function which takes the values -1, 0 or +1 depending on the prime factorisation of its input n.
^{[e]} - Tau function [r]: An arithmetic function studied by Ramanjuan, the coefficients of the q-series expansion of the modular form Delta.
^{[e]} - Convolution [r]: A process which combines two functions on a set to produce another function on the set: the value of the product function depends on a range of values of the argument.
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