Physical mathematics in number theory

DOI10.1007/s11853-010-0044-5zbMath1253.11081OpenAlexW2092560430WikidataQ100935416 ScholiaQ100935416MaRDI QIDQ644498

Anatolii A. Karatsuba, Ekatharine A. Karatsuba

Publication date: 4 November 2011

Published in: Functional Analysis and Other Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11853-010-0044-5

zbMATH Keywords

Riemann zeta functionapproximationDirac theorytrigonometric series\(\pi\)-functiontheory of prime numbersUniverse expansion

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Other Dirichlet series and zeta functions (11M41) Miscellaneous applications of number theory (11Z05)

Related Items

On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s ⋮ Dirac electron free field anticommutator and its zeros on time intervals ⋮ The mean square of the Pauli-Jordan-Dirac anticommutator with respect to spatial variables

Uses Software

• OEIS

Cites Work

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• On the Riemann asymptotic formula for \(\pi(x)\)
• Approximation of exponential sums by shorter ones
• On an approach to the study of the Jaynes-Cummings sum in quantum optics
• Application of ATS in a Quantum-optical Model
• Approximation of sums of oscillating summands in certain physical problems
• Computing π(x): The Meissel-Lehmer Method
• On the Sign of the Difference π(x) - li(x)
• On the Difference π(x )-li(x ) (I)
• A new bound for the smallest $x$ with $\pi(x) > \mathrm{li}(x)$
• On the difference π(x) - li(x)

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