: Mathematics: local zeta function

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geometry > algebraic geometry > algebraic variety > local zeta function

number > number theory > analytic number theory > L-function > local zeta function

mathematical analysis > complex analysis > meromorphic function > L-function > local zeta function

local zeta function

In number theory, the local zeta function $Z (V, s)$ (sometimes called the congruent zeta function or the Hasse–Weil zeta function) is defined as
${\\displaystyle Z(V,s)=\\exp \\left(\\sum _{m=1}^{\\infty }{\ rac {N_{m}}{m}}(q^{-s})^{m}\ ight)}$
where $V$ is a non-singular $n$ -dimensional projective algebraic variety over the field $F q$ with $q$ elements and $N m$ is the number of points of $V$ defined over the finite field extension $F q m$ of $F q$ .
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Local_zeta_function)

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