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math.NT2023
On a Weighted Series of the Hurwitz Zeta Function
Matthew Fox, Chaitanya Karamchedu
In this note we prove that for all , , and with , the (alternating) weighted series of the Hurwi…
math.NT2020
On Ramanujan Sums of a Real Variable and a New Ramanujan Expansion for the Divisor Function
Matthew S. Fox, Chaitanya Karamchedu
We show that the absolute convergence of a Ramanujan expansion does not guarantee the convergence of its real variable generalization, which is obtained by replacing the integer ar…