On certain trigonometric sums in several variables
The concept of even functions \(\text{mod } r\) and of totally even functions is due to \textit{E. Cohen} [Am. Math. Mon. 66, 105-117 (1959; Zbl 0084.270) or Trans. Am. Math. Soc. 96, 355-381 (1960); Erratum, ibid. 102, 545 (1962; Zbl 0121.050)]. In the first part of the present paper the authors describe the Hilbert space structure of these functions. Further they introduce the function \(\varepsilon_k\) as a new generalization of Dedekind's \(\psi\)-function. Using the notion of totally even functions and the function \(\varepsilon_k\) the authors prove a \(k\)-dimensional extension of an identity of \textit{P. Kesava Menon} [J. Indian Math. Soc., New Ser. 29, 155-163 (1965; Zbl 0144.277)].
scientific article; zbMATH DE number 761845