### An Upper Bound for the Whittaker Constant W

Journal of the London Mathematical Society, Vol. 22 (1947), 305-311

Received 2 September, 1947; read 16 October, 1947.

Introduction

Let f(z) be an integral function whose maximum modulus satisfies

and such that f(z) and all its derivatives have each at least one zero on or within the circle |z| = ρ. The Whittaker constant W is the lower bound of these numbers ρ for which at least one such f(z) exists not identically zero. Whittaker and Boas use equivalent definitions. Levinson and Boas proved that

0.7199 < W < 0.7399,

while Pondiczery conjectured that W = 2*e*^{–1} = 0.7357.... In this note I show that W < 0.7378, thus reducing the length of the interval in which W is known to lie by about 10 per cent.

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