On the Order of Growth of Lerch Zeta Functions
Mathematics, 2023 We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t13/84+ϵ as t → ∞.
Jörn Steuding, Janyarak Tongsomporn
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Moments of the Riemann zeta function [PDF]
, 2006 Assuming the Riemann hypothesis, we obtain an upper bound for the moments of the Riemann zeta function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for these moments.
K. Soundararajan
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SHARP UPPER BOUNDS FOR FRACTIONAL MOMENTS OF THE RIEMANN ZETA FUNCTION [PDF]
Quarterly Journal of Mathematics, 2019 We establish sharp upper bounds for the $2k$th moment of the Riemann zeta function on the critical line, for all real $0 \leqslant k \leqslant 2$. This improves on earlier work of Ramachandra, Heath-Brown and Bettin–Chandee–Radziwiłł.
W. Heap +2 more
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An approximation to zeros of the Riemann zeta function using fractional calculus [PDF]
Mathematics and Statistics, 2020 A novel iterative method to approximate the zeros of the Riemann zeta function is presented. This iterative method, valid for one and several variables, uses the properties of fractional calculus, in particular the fact that the fractional derivatives of
A. Torres-Hernandez, F. Brambila-Paz
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Complete basis set extrapolation of electronic correlation energies using the Riemann zeta function. [PDF]
Journal of Chemical Theory and Computation, 2019 In this communication we demonstrate the effectiveness of the method of complete basis set (CBS) extrapolation of correlation energies based on the application of the Riemann zeta function.
M. Lesiuk, B. Jeziorski
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Precalculated arrays-based algorithms for the calculation of the Riemann zeta-function
Vilnius University Open Series, 2022 In this paper, we continue the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. We introduce two precalculated arrays-based modifications of MB-method.
Lukas Kuzma +2 more
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Decoupling, exponential sums and the Riemann zeta function [PDF]
, 2014 We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H].
J. Bourgain
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New Results Involving Riemann Zeta Function Using Its Distributional Representation
Fractal and Fractional, 2022 The relation of special functions with fractional integral transforms has a great influence on modern science and research. For example, an old special function, namely, the Mittag–Leffler function, became the queen of fractional calculus because its ...
Asifa Tassaddiq, Rekha Srivastava
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Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function [PDF]
Journal of the London Mathematical Society, 2020 We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high moments of this object.
Marco Aymone, W. Heap, J. Zhao
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Quantization of the Riemann Zeta-Function and Cosmology [PDF]
, 2007 Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field theories.
Barnaby N. +18 more
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