Vol. 60, No. 1, 1975

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Rational valued series of exponentials and divisor functions

Emil Grosswald

Vol. 60 (1975), No. 1, 111–114

Recently A. Terras established some (soon to be published) relations between the values of Riemann’s zeta function at consecutive positive integral argument and values of certain modified Bessel functions. By combining these relations with some previous results concerning the values of ζ(s) at odd, positive integers (Grosswald-Nachrichten Akad. Wiss. Göttingen, II Math.-Phys. Klasse 1970, pp. 9–13) it follows that certain infinite series of exponentials and divisor functions (somewhat reminiscent of Lambert series) are rational valued.

Mathematical Subject Classification
Primary: 10H05
Received: 23 March 1974
Published: 1 September 1975
Emil Grosswald