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math.NT2024
Evaluations and relations for finite trigonometric sums
Bruce C. Berndt, Sun Kim, Alexandru Zaharescu
Several methods are used to evaluate finite trigonometric sums. In each case, either the sum had not previously been evaluated, or it had been evaluated, but only by analytic means…
math.NT2016
On a theorem of A. I. Popov on sums of squares
Bruce C. Berndt, Atul Dixit, Sun Kim +1
Let denote the number of representations of the positive integer as the sum of squares. In 1934, the Russian mathematician A.~I.~Popov stated, but did not rigorous…