Extreme values of ζ′(ρ)

By Nathan Ng. 2007

362 citations recorded by the source corpus.

Assuming the Riemann hypothesis, we exhibit large and small values of the derivative of the zeta function evaluated at the non‐trivial zeros of the zeta function. These results are proved by applying Soundararajan's resonance method.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a16606b975c6c9f30bca0281a74b73057f60e3fb

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Tail asymptotics for the sum of two heavy-tailed dependent risks (2006, background): “A natural extremal dependence measure in this setting is ρ := 1 − 1 (π/4)2 ∫ π/2 0 ( ϕ − π 4 )2 S(dϕ), see Resnick [27].”
PSEUDO-MATHEMATICS AND FINANCIALCHARLATANISM: THE EFFECTS OF BACKTEST OVERFITTING ONOUT-OF-SAMPLE PERFORMANCE (2014, neutral): “The normalizing constants (α,β) are derived in Resnick [22] and Embrechts et al.”
Causal discovery in heavy-tailed models (2019, background): “On the other hand, the statistics of univariate extremes is relatively well understood (Resnick (2008)) and there is a large set of tools for the analysis of heavy-tailed distributions.”
Asymptotic Results for the Sum of Dependent Non-identically Distributed Random Variables (2009, methodology): “We can use the same method as described in [17] to get a random vector (X1, X2) which has regularly varying marginal distributions F1(x) and F2(x) with limu→∞ F1(x)/F2(x) = 1, but it is not multivariate regularly varying and hence the copula C defined by (X1, X2) is not in the maximum domain of attr”
Tail dependence functions and vine copulas (2010, background): “, Xd) is usually assumed to ensure the existence of such limits [15,16]; this comment applies as well to limits that appear later.”
Convergence to Lévy stable processes under some weak dependence conditions (2009, methodology): “For a comprehensive account on this subject in the independent case, we refer the reader to the expository article by Resnick [38] and to his recent monograph [40].”
Blow-up rates of large solutions for elliptic equations☆ (2010, methodology): “[30] S.I. Resnick, Extreme Values, Regular Variation, and Point Processes, Springer-Verlag, New York, 1987.”
A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations With Inverse Square Potentials (2014, background): “For examples and properties of Γ-varying functions, we refer to [5], [17], [20] or [31].”
Boundary blow-up elliptic problems with nonlinear gradient terms☆ (2006, background): “Let Ψ be nondecreasing on R, we define (as in [36]) the inverse of Ψ by”
Topics in Occupation Times and Gaussian Free Fields (2012, background): “5) We refer to [20], [22] for a more detailed discussion of Poisson point measures.”
REGULAR VARIATION FOR MEASURES ON METRIC SPACES (2006, background): “[20]) and of solutions to random difference equations (see e.”
Extremes of independent Gaussian processes (2009, methodology): “The process LΓ is max-infinitely divisible, which means (see [14] for a definition) that for every k ∈ N, we can represent LΓ as a pointwise minimum of k independent identically distributed processes.”
The functional equation of the smoothing transform (2009, background): “value theory [36], where they can be interpreted as generalizations of the distributional equations of stability and min-stability, respectively.”
Ergodic properties of max-infinitely divisible processes (2009, background): “distributions (and processes) were introduced in [1] and studied in [28, 18, 5].”