Bruce C. Berndt

collaborators

2 papers

math.NT2025

An Arithmetic Sum Associated with the Classical Theta Function

Bruce C. Berndt, Raghavendra N. Bhat, Jeffrey L. Meyer +2

The sum $S (h, k) := \sum_{j = 1}^{k - 1} (- 1)^{j + 1 + [hj / k]}$ appears in the modular transformation formulae of the classical theta function $ϑ_{3} (z)$ . The double sum $S(k) := \sum_{h…

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…