In mathematics, and more particularly in analytic number theory, Perron's formula is a formula discovered by Oskar Perron to calculate the sum of an arithmetic function, by means of an inverse Mellin transform. == Statement == Let { a ( n ) } {\displaystyle \{a(n)\}} be an arithmetic function, and let g ( s ) = ∑ n = 1 ∞ a ( n ) n s {\displaystyle g(s)=\sum _{n=1}^{\infty }{\frac {a(n)}{n^{s}}}} be the corresponding Dirichlet series.
In mathematics, and more particularly in analytic number theory, Perron's formula is a formula discovered by Oskar Perron to calculate the sum of an arithmetic function, by means of an inverse Mellin transform. == Statement == Let { a ( n ) } {\displaystyle \{a(n)\}} be an arithmetic function, and let g ( s ) = ∑ n = 1 ∞ a ( n ) n s {\displaystyle g(s)=\sum _{n=1}^{\infty }{\frac {a(n)}{n^{s}}}} be the corresponding Dirichlet series.
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