Mary L. Cartwright

The Zeros of Certain Integral Functions (II)
Quarterly Journal of Mathematics, Vol. 2 (1931), 113-129

Introduction (Excerpts)

In a previous paper I considered functions of the form

where φ(t) is a complex function, integrable in the sense of Lebesgue, and φ(t) tends to a finite limit other than 0 at each end. The object of this paper is to consider the cases in which φ(t) tends to 0 or ∞ at one or both ends. If φ(t) —> ∞ as t —> ±1, we need lighter restrictions in order to obtain equivalent results, and if φ(t) —> 0, heavier ones, as the following example shows.

---