Pfluger, the son of a farmer, attended secondary school in
Stans. He then studied mathematics at
ETH Zürich, where in 1935 he received his promotion (Ph.D) under
George Pólya with a thesis ''Über eine Interpretation gewisser Konvergenz- und Fortsetzungseigenschaften Dirichlet'scher Reihen
. Afterwards, he became a Gymnasium'' teacher at the canton school in
Zug and the canton school in
Solothurn. He received his habilitation qualification in 1938 and in 1939 became a professor extraordinarius for applied mathematics and mathematical physics at the
University of Fribourg. At ETH Zürich he became a professor extraordinarius in 1940 and in 1943 a professor ordinarius in the professorial chair vacated by George Pólya in 1940. Pfluger retired from ETH Zürich in 1978 as professor emeritus. He did research on the
value distribution theory of
Rolf Nevanlinna,
potential theory,
conformal maps and
quasiconformal mapping, as well as
Riemann surfaces. In 1957 Pfluger's monograph
Theorie der Riemannschen Flächen was published in
Springer's series
Grundlehren der mathematischen Wissenschaften. With Joseph Hersch, he introduced in 1952 a function (now called the Hersch-Pfluger distortion function) useful in estimating the distortion of quasiconformal mappings. Entire functions with certain regularity properties were introduced and extensively studied by Pfluger and
Boris Levin; these functions are now referred to as functions of completely regular growth in the sense of Levin and Pfluger. Pfluger served a two-year term as president of the
Swiss Mathematical Society in 1950–1951. In 1973 he was elected a foreign member of the
Finnish Academy of Sciences. His doctoral students include
Peter Henrici and
Heinz Rutishauser. Pfluger was married since 1938 to Maria Jeger. ==Selected publications==