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Beurling zeta function : ウィキペディア英語版
Beurling zeta function
In mathematics, a Beurling zeta function is an analogue of the Riemann zeta function where the ordinary primes are replaced by Beurling generalized primes: a sequence of real numbers greater than 1 that tend to infinity. These were introduced by .
A Beurling generalized integer is a number that can be written as a product of Beurling generalized primes. Beurling generalized the usual prime number theorem to Beurling generalized primes. He showed that if the number ''N''(''x'') of Beurling generalized integers less than ''x'' is of the form ''N''(''x'') = ''Ax'' + O(''x'' log−''γ''''x'') with ''γ'' > 3/2 then the number of Beurling generalized primes less than ''x'' is asymptotic to ''x''/log ''x'', just as for ordinary primes,
but if ''γ'' = 3/2 then this conclusion need not hold.
==See also==

* Abstract analytic number theory

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