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An Approximation of the Prime Counting Function and a New Representation of the Riemann Zeta Function

open access: yesMathematics
Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuable.
Timothy Ganesan
doaj   +1 more source

Alternating series in terms of Riemann zeta function and Dirichlet beta function

open access: yesElectronic Research Archive
By making use of the multisection series method, four classes of alternating infinite series are evaluated, in closed form, by the Riemann zeta function and the Dirichlet beta function.
Zhiling Fan, Wenchang Chu
doaj   +1 more source

Serendipity strikes again. [PDF]

open access: yesProc Natl Acad Sci U S A, 2022
Grünbaum FA.
europepmc   +1 more source

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