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math.NT2025
On an spt function for the -th symmetrized crank function
Alexander E. Patkowski
In this paper we find the smallest part function related to the -th symmetrized crank function, corresponding to the one obtained in Patkowski [11] for the -th symmetrized ra…
math.NT2025
An application of Titchmarsh's theorem and the Salem equivalence
Alexander E. Patkowski
We extend the equivalence of the Salem type for the Riemann hypothesis by application of Titchmarsh's theorem. Other equivalences to the Riemann hypothesis and notes on related Fou…
math.NT2025
On certain sums over primes and the Riesz function
Alexander E. Patkowski
We offer some comments on series involving the Mbius function which approximate sums over primes. To accomplish this, we utilize the derivative of the Gram series by appl…