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 . References 1953 introductions 1953 in science Alan Turing Zeta and L-functions