Chaitanya Karamchedu

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20202026

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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 $a \in N$ , $x \in R_{+} \cup {0}$ , and $s \in C$ with $ℜ (s) > a + 2$ , 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…