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On the minimum modulus of integral functions

1934/10/01 by M. L. Cartwright · 1 citation
Mathematics · #Analytic Number Theory Research #Analytic and geometric function theory #Meromorphic and Entire Functions

paper · doi:10.1017/s0305004100012652

openalex publication_date 1934/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/27

Abstract

1·1. Let f ( z ) be an integral function of order ρ, and let It is well known that, if ρ < 1, This result was first conjectured by Littlewood, who proved it with cos 2πρ in place of cosπρ; it was afterwards proved independently by Wiman and Valiron about the same time. Many other authors have written on the subject, considering among other things the set of valves of r for which m ( r ) is comparatively large.

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