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math.NT2023
On near orthogonality of certain -vectors involving generalized Ramanujan sums
Neha Elizabeth Thomas, K Vishnu Namboothiri
The near orthgonality of certain -vectors involving the Ramanujan sums were studied by E. Alkan in [J. Number Theory, 140:147--168 (2014)]. Here we undertake the study of simila…
math.NT2023
A computable formula for evaluating the mean square sum of -functions
Neha Elizabeth Thomas, K Vishnu Namboothiri
For Dirichlet characters mod where , we here give a computable formula for evaluating the mean square sums $\sum\limits_{\substack{χ\text{ mod }k\\χ(-1)=(-1)^r}}|L…
math.NT2023
On an exponential power sum
Neha Elizabeth Thomas, K Vishnu Namboothiri
Using combinatorial techniques, we derive a recurrence identity that expresses an exponential power sum with negative powers in terms of another exponential power sum with positive…