On a Nearly Forgotten Polynomial Result by P. Bohl

Abstract

Piers Bohl (1865-1921) was an outstanding Latvian mathematician whose name is particularly connected with several crucial achievements that were ahead of their time. Unfortunately, the contemporary mathematical community did not recognize their significance. This paper discusses one of Bohl's results from 1908 that remained nearly unnoticed, even up until the present. It concerns a general complex trinomial and answers the problem of the distribution of its roots with respect to a given modulus. During the last few decades, this and other related problems have been extensively studied in numerous particular cases, without knowledge of this existing answer. This paper recalls the aforementioned Bohl's result and illustrates how easily it can imply conclusions of recent as well as older works regarding this topic.Piers Bohl (1865-1921) was an outstanding Latvian mathematician whose name is particularly connected with several crucial achievements that were ahead of their time. Unfortunately, the contemporary mathematical community did not recognize their significance. This paper discusses one of Bohl's results from 1908 that remained nearly unnoticed, even up until the present. It concerns a general complex trinomial and answers the problem of the distribution of its roots with respect to a given modulus. During the last few decades, this and other related problems have been extensively studied in numerous particular cases, without knowledge of this existing answer. This paper recalls the aforementioned Bohl's result and illustrates how easily it can imply conclusions of recent as well as older works regarding this topic.