Jan Popken

Jan Popken (born December 14, 1905 in Smilde , † August 6, 1970 in Amsterdam ) was a Dutch mathematician who dealt with number theory .

Popken received his doctorate in 1935 from the University of Groningen under Johannes van der Corput ( on arithmetic properties of analytical functions ). In 1937 he received his habilitation in Groningen ( Over het rekenkundig karakter van getalen ) and was a private lecturer there until 1940. 1940 to 1942 he was a private lecturer in Leiden and from 1947 professor at the University of Utrecht and from 1955 at the University of Amsterdam .

Among other things, he dealt with transcendent numbers , so in 1929 he gave a transcendence measure for Euler's number e. He specifically proved that for a polynomial P (integer coefficients) of degree n and maximum magnitude the coefficient H (also called height , H is greater than or equal to 3) applies:

{\ displaystyle | P (e) |> {\ frac {1} {H ^ {n + {\ frac {c} {\ log \ log H}}}}}}

with a constant c that only depends on n. He also set up a transcendence measure for and with Jurjen Koksma from . ${\ displaystyle \ pi}$ ${\ displaystyle e ^ {\ pi}}$

In 1954 he became a member of the Royal Netherlands Academy of Sciences.

His doctoral students include Gerrit Lekkerkerker , Robert Tijdeman and Abraham van der Sluis .

Fonts

On the transcendence of e, Mathematische Zeitschrift, 29, 1929, 525-541, online

On the transcendence of , Mathematische Zeitschrift, 29, 1929, 542-548, online ${\ displaystyle \ pi}$
Sur la nature arithmétique du nombre e, Comptes Rendus Acad. Sci., Paris, 186, 1928, 1505-1507
with Jurjen Koksma On the transcendence of , J. Reine Angew. Math., 168, 1932, 211-230, online ${\ displaystyle e ^ {\ pi}}$

Web links

Individual evidence

↑ Jan Popken in the Mathematics Genealogy Project (English)
^ Theodor Schneider Introduction to the transcendent numbers , Springer Verlag 1957, pp. 88f

personal data
SURNAME	Popken, Jan
BRIEF DESCRIPTION	Dutch mathematician
DATE OF BIRTH	December 14, 1905
PLACE OF BIRTH	Smilde
DATE OF DEATH	August 6, 1970
Place of death	Amsterdam

[1] Jan Popken in the Mathematics Genealogy Project (English)

[2] Theodor Schneider Introduction to the transcendent numbers , Springer Verlag 1957, pp. 88f