List of zeta functions

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a <a href="/facts/Zeta/FrAnlRnX">zeta</a> function is (usually) a <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> analogous to the original example, the <a href="/facts/Riemann_zeta_function/MnfRu7lY">Riemann zeta function</a>

ζ
        (
        s
        )
        =
        
          ∑
          
            n
            =
            1
          
          
            ∞
          
        
        
          
            1
            
              n
              
                s
              
            
          
        
        .
      
    
    {\displaystyle \zeta (s)=\sum _{n=1}^{\infty }{\frac {1}{n^{s}}}.}

Zeta functions include:

<ul><li><a href="/facts/Airy_zeta_function/rSuwQcnF">Airy zeta function</a>, related to the zeros of the <a href="/facts/Airy_function/bydfB54Y">Airy function</a></li>
<li><a href="/facts/Arakawa%25E2%2580%2593Kaneko_zeta_function/4E0WzbVW">Arakawa–Kaneko zeta function</a></li>
<li><a href="/facts/Arithmetic_zeta_function/yP1wFGnK">Arithmetic zeta function</a></li>
<li><a href="/facts/Artin%25E2%2580%2593Mazur_zeta_function/vaR7IcvR">Artin–Mazur zeta function</a> of a dynamical system</li>
<li><a href="/facts/Barnes_zeta_function/6k542ToH">Barnes zeta function</a> or double zeta function</li>
<li><a href="/facts/Beurling_zeta_function/br9wdyDe">Beurling zeta function</a> of Beurling generalized primes</li>
<li><a href="/facts/Dedekind_zeta_function/Nj8PwFo8">Dedekind zeta function</a> of a number field</li>
<li>Duursma zeta function of error-correcting codes</li>
<li><a href="/facts/Real_analytic_Eisenstein_series/rbRn4zpU">Epstein zeta function</a> of a quadratic form</li>
<li><a href="/facts/Goss_zeta_function/oLBJXNyk">Goss zeta function</a> of a function field</li>
<li><a href="/facts/Hasse%25E2%2580%2593Weil_zeta_function/1THWBhB2">Hasse–Weil zeta function</a> of a variety</li>
<li><a href="/facts/Height_zeta_function/4B6kwedM">Height zeta function</a> of a variety</li>
<li><a href="/facts/Hurwitz_zeta_function/4EH7sKXB">Hurwitz zeta function</a>, a generalization of the Riemann zeta function</li>
<li><a href="/facts/Igusa_zeta_function/5sG7AxF9">Igusa zeta function</a></li>
<li><a href="/facts/Ihara_zeta_function/1FJ8MMr9">Ihara zeta function</a> of a graph</li>
<li><a href="/facts/L-function/REVCKvU7">L-function</a>, a "twisted" zeta function</li>
<li><a href="/facts/Lefschetz_zeta_function/IgqQ8m2a">Lefschetz zeta function</a> of a morphism</li>
<li><a href="/facts/Lerch_zeta_function/26RvsFok">Lerch zeta function</a>, a generalization of the Riemann zeta function</li>
<li><a href="/facts/Local_zeta_function/jIu1cg89">Local zeta function</a> of a characteristic-p variety</li>
<li><a href="/facts/Matsumoto_zeta_function/rlCovAAH">Matsumoto zeta function</a></li>
<li><a href="/facts/Minakshisundaram%25E2%2580%2593Pleijel_zeta_function/dwThxTA9">Minakshisundaram–Pleijel zeta function</a> of a Laplacian</li>
<li><a href="/facts/Motivic_zeta_function/kXxnr7Gd">Motivic zeta function</a> of a motive</li>
<li><a href="/facts/Multiple_zeta_function/tBycfN4h">Multiple zeta function</a>, or Mordell–Tornheim zeta function of several variables</li>
<li><a href="/facts/P-adic_L-function/9LE4oSTW">p-adic zeta function</a> of a p-adic number</li>
<li><a href="/facts/Prime_zeta_function/XS4sa1zn">Prime zeta function</a>, like the Riemann zeta function, but only summed over primes</li>
<li><a href="/facts/Riemann_zeta_function/MnfRu7lY">Riemann zeta function</a>, the archetypal example</li>
<li><a href="/facts/Ruelle_zeta_function/prssMear">Ruelle zeta function</a></li>
<li><a href="/facts/Selberg_zeta_function/DfgbLy7F">Selberg zeta function</a> of a <a href="/facts/Riemann_surface/qoj8ogv8">Riemann surface</a></li>
<li><a href="/facts/Shimizu_L-function/VmN46psm">Shimizu L-function</a></li>
<li><a href="/facts/Shintani_zeta_function/QCFWDa7p">Shintani zeta function</a></li>
<li>Subgroup zeta function</li>
<li><a href="/facts/Witten_zeta_function/r2sj3X0m">Witten zeta function</a> of a Lie group</li>
<li><a href="/facts/Incidence_algebra/xrLTmg99">Zeta function of an incidence algebra</a>, a function that maps every interval of a poset to the constant value 1. Despite not resembling a holomorphic function, the special case for the poset of integer divisibility is related as a formal Dirichlet series to the Riemann zeta function.</li>
<li><a href="/facts/Zeta_function_(operator)/WFYFgfun">Zeta function of an operator</a> or spectral zeta function</li></ul>

List of zeta functions open-in-new

List of zeta functions