Abstract
It follows from the asymptotic formula for π(x) (Theorem 5 of Chapter VI) that there exists at least one prime number in every interval (x, x + y), where x > x 0>0 and
An application of the Theorem on the density distribution of the zeros of the zeta function in the critical strip enables us to obtain a much stronger result (cf. the corollary of Theorem 2).
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© 1993 Springer-Verlag Berlin Heidelberg
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Karatsuba, A.A., Nathanson, M.B. (1993). The Density of the Zeros of the Zeta Function and the Problem of the Distribution of Prime Numbers in Short Intervals. In: Basic Analytic Number Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58018-5_7
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DOI: https://doi.org/10.1007/978-3-642-58018-5_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-63436-9
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