Introduction To Analytic And Probabilistic Number Theory

By J. Eichel. 2016

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Sums of Kloosterman sums in arithmetic progressions, and the error term in the dispersion method (2015, unknown): “Quoting from [ Ten95 , Theorem I.5.4] the bound ϕ ( q ) q/ log log q , we obtain The sum over q 1 , q 2 is O (1 / ( r 2 d 1 d 2 )).”
Hyperuniform states of matter (2018, background): “On the other hand, it is well known that the prime numbers are directly linked to the zeros of the Riemann zeta function via explicit formulas [228].”
THE LOGARITHMICALLY AVERAGED CHOWLA AND ELLIOTT CONJECTURES FOR TWO-POINT CORRELATIONS (2015, methodology): “Applying the Halasz inequality (see for example [32] or [12, Corollary 1]) we conclude that 1 y ∑”
Multiplicative functions in short intervals (2015, unknown): “It is well known that the number of X1/u smooth numbers up to X is asymptotically ρ(u)X, with ρ(u) denoting the Dickman-de Bruijn function [38].”
The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line (2016, background): “The books [81, 48, 80], among many others, are excellent references for further properties of the Riemann zeta function.”
Mod-ϕ Convergence (2016, methodology): “The Selberg-Delange method allows to extract from this formula precise estimates for the generating function of ωn; see [Ten95] and references therein.”