On the Nature of γ-th Arithmetic Zeta Functions [PDF]
Symmetry, 2020 Symmetry and elementary symmetric functions are main components of the proof of the celebrated Hermite–Lindemann theorem (about the transcendence of e α , for algebraic values of α ) which settled the ancient Greek problem of squaring the circle. In this paper, we are interested in similar results, but for powers such as e γ log n
Pavel Trojovský
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Arithmetic equivalence for function fields, the Goss zeta function and a generalization [PDF]
Journal of Number Theory, 2009 A theorem of Tate and Turner says that global function fields have the same zeta function if and only if the Jacobians of the corresponding curves are isogenous. In this note, we investigate what happens if we replace the usual (characteristic zero) zeta function by the positive characteristic zeta function introduced by Goss.
Gunther Cornelissen +2 more
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Riemann zeta function and arithmetic progression of higher order [PDF]
Notes on Number Theory and Discrete Mathematics, 2020 Riemann zeta function has a great importance in number theory, constituting one of the most studied functions. The zeta function, being a series, has a close relationship with the arithmetic progressions (AP).
Hamilton Brito +2 more
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Numerical Integration of Slater Basis Functions Over Prolate Spheroidal Grids. [PDF]
J Comput ChemAtom‐centered Slater functions are integrated over a prolate spheroidal grid, allowing the use of larger basis sets in correlated electronic structure computations. ABSTRACT Slater basis functions have desirable properties that can improve electronic structure simulations, but improved numerical integration methods are needed. This work builds upon the
Stark A +5 more
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Mean-square values of the Riemann zeta function on arithmetic progressions
Monatshefte für Mathematik, 2023 Comment: This is an updated version of arXiv:2212.06520.
Hirotaka Kobayashi
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A Two-Stage Cascading Amplification Strategy Based on Zn<sup>2+</sup>-Doped WO<sub>X</sub> Nanozymes for Ultrasensitive Lateral Flow Immunoassays of Clostridium Difficile Toxin B. [PDF]
Adv Sci (Weinh)Based on the modulation of active sites and electronic structure of substrate materials, along with a colorimetric two‐stage cascading enhancement strategy, an LFIA platform with highly efficient POD‐mimetic enzymes is developed, achieving highly sensitive detection of Clostridium difficile toxin B.
Su J +6 more
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Discrete Ω-results for the Riemann zeta function [PDF]
Forum mathematicum, 2023 We study lower bounds for the Riemann zeta function ζ ( s ) {\zeta(s)} along vertical arithmetic progressions in the right-half of the critical strip.
Paolo Minelli, Athanasios Sourmelidis
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On the General Divergent Arithmetic Sums over the Primes and the Symmetries of Riemann’s Zeta Function [PDF]
SymmetryIn this paper, we address the problem of the divergent sums of general arithmetic functions over the set of primes. In classical analytic number theory, the sum of the logarithm of the prime numbers plays a crucial role. We consider the sums of powers of
L. Acedo
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A Further Generalisation of Sums of Higher Derivatives of the Riemann Zeta Function [PDF]
International Journal of Number Theory, 2021 We prove an asymptotic for the sum of $\zeta^{(n)} (\rho)X^{\rho}$ where $\zeta^{(n)} (s)$ denotes the $n$th derivative of the Riemann zeta function, $X$ is a positive real and $\rho$ denotes a non-trivial zero of the Riemann zeta function.
Andrew Pearce‐Crump
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