**Pair correlation estimates for the zeros of the zeta function via semidefinite programming.** / Chirre, Andrés ; Goncalves, Felipe; de Laat, David.

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Chirre, A, Goncalves, F & de Laat, D 2020, 'Pair correlation estimates for the zeros of the zeta function via semidefinite programming', *Advances in Mathematics*, vol. 361, 106926, pp. 1-22. https://doi.org/10.1016/j.aim.2019.106926

Chirre, A., Goncalves, F., & de Laat, D. (2020). Pair correlation estimates for the zeros of the zeta function via semidefinite programming. *Advances in Mathematics*, *361*, 1-22. [106926]. https://doi.org/10.1016/j.aim.2019.106926

Chirre A, Goncalves F, de Laat D. Pair correlation estimates for the zeros of the zeta function via semidefinite programming. Advances in Mathematics. 2020 Feb 12;361:1-22. 106926. https://doi.org/10.1016/j.aim.2019.106926

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title = "Pair correlation estimates for the zeros of the zeta function via semidefinite programming",

abstract = "In this paper we study the distribution of the non-trivial zeros of the Riemann zeta-function (and other L-functions) using Montgomery's pair correlation approach. We use semidefinite programming to improve upon numerous asymptotic bounds in the theory of the zeta-function, including the proportion of distinct zeros, counts of small gaps between zeros, and sums involving multiplicities of zeros.",

keywords = "Pair correlation, Semidefinite programming, Zeta function, Zeta zeros",

author = "Andr{\'e}s Chirre and Felipe Goncalves and {de Laat}, David",

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AB - In this paper we study the distribution of the non-trivial zeros of the Riemann zeta-function (and other L-functions) using Montgomery's pair correlation approach. We use semidefinite programming to improve upon numerous asymptotic bounds in the theory of the zeta-function, including the proportion of distinct zeros, counts of small gaps between zeros, and sums involving multiplicities of zeros.

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KW - Semidefinite programming

KW - Zeta function

KW - Zeta zeros

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