About: Turing's method

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In mathematics, Turing's method is used to verify that for any given Gram point gm there lie m + 1 zeros of ζ(s), in the region 0 < Im(s) < Im(gm), where ζ(s) 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 i < n we find a list of Gram points and a complementary list , where gi is the smallest number such that and Then the bound is achieved and we have that there are exactly m + 1 zeros of ζ(s), in the region 0 < Im(s) < Im(gm).

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  • In mathematics, Turing's method is used to verify that for any given Gram point gm there lie m + 1 zeros of ζ(s), in the region 0 < Im(s) < Im(gm), where ζ(s) 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 i < n we find a list of Gram points and a complementary list , where gi is the smallest number such that where Z(t) is the Hardy Z function. Note that gi 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 ζ(s), in the region 0 < Im(s) < Im(gm). (en)
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  • In mathematics, Turing's method is used to verify that for any given Gram point gm there lie m + 1 zeros of ζ(s), in the region 0 < Im(s) < Im(gm), where ζ(s) 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 i < n we find a list of Gram points and a complementary list , where gi is the smallest number such that and Then the bound is achieved and we have that there are exactly m + 1 zeros of ζ(s), in the region 0 < Im(s) < Im(gm). (en)
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  • Turing's method (en)
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