In mathematics, Turing's method is used to verify that for any given Gram point there lie m + 1 zeros of , in the region , where is the Riemann zeta function. It was discovered by Alan Turing and published in 1953, although that proof contained errors and a correction was published in 1970 by R. Sherman Lehman.
For every integer i with we find a list of Gram points and a complementary list , where is the smallest number such that
where Z(t) is the Hardy Z function. Note that may be negative or zero. Assuming that and there exists some integer k such that , then if
and
Then the bound is achieved and we have that there are exactly m + 1 zeros of , in the region .