Results 31 to 40 of about 6,967 (160)
A new generalization of the Riemann zeta function and its difference equation
Advances in Difference Equations, 2011 We have introduced a new generalization of the Riemann zeta function. A special case of our generalization converges locally uniformly to the Riemann zeta function in the critical strip.
Qadir Asghar +2 more
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An In-Depth Investigation of the Riemann Zeta Function Using Infinite Numbers
MathematicsThis study focuses on an in-depth investigation of the Riemann zeta function. For this purpose, infinite numbers and rotational infinite numbers, which have been introduced in previous studies published by the author, are used.
Emmanuel Thalassinakis
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Complexity, 2021 In this paper, authors prove new variants of Hermite–Jensen–Mercer type inequalities using ψ–Riemann–Liouville fractional integrals with respect to another function via convexity.
Saad Ihsan Butt +4 more
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Moments of the Riemann zeta function [PDF]
Annals of Mathematics, 2009 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. The method extends to moments in families of $L$-functions.
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The delta-shock wave for the two variables of a class of Temple system
Advances in Difference Equations, 2018 We investigate the Riemann problem for one-dimensional Temple class, obtain the Riemann solutions containing delta-shock wave, and discover that each variable of this system contains the Dirac delta function in different region. By the interaction of the
Guodong Wang +3 more
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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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Log-tangent integrals and the Riemann zeta function
Mathematical Modelling and Analysis, 2019 We show that integrals involving the log-tangent function, with respect to any square-integrable function on , can be evaluated by the harmonic series. Consequently, several formulas and algebraic properties of the Riemann zeta function at odd positive ...
Lahoucine Elaissaoui +1 more
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The Nevanlinna Functions of the Riemann Zeta-Function
Journal of Mathematical Analysis and Applications, 1999 The author computes the Nevanlinna characteristic function, the Nevanlinna deficiencies for each \(a\) in \(\mathbb{C}\cup \{\infty\}\) and the Nevanlinna counting functions for the Riemann zeta-function. These results are of special interest because of the recent discovery of analogies between number theory and Nevanlinna theory.
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