Harald Bohr

Harald August Bohr (born April 22, 1887 in Copenhagen , † January 22, 1951 in Gentofte ) was a Danish mathematician and football player .

life and work

Harald Bohr was the son of the Danish physiologist Christian Bohr , his brother was the physicist Niels Bohr . Bohr's research areas were in function theory and analytical number theory .

From 1904 he studied mathematics at the University of Copenhagen . Initially, Bohr also pursued a career as an athlete. In addition to his skills as a scientist, he was considered one of the best footballers of his time: Bohr was a member of the Danish national team and won the silver medal at the 1908 Summer Olympics ; together with his brother he was active for the Akademisk Boldklub association.

In 1910 he received his doctorate in Copenhagen (with Edmund Landau , contributions to the theory of the Dirichlet series ) and spent a few months in Göttingen near Landau. The defense of his doctoral thesis is said to have been attended by spectators interested in football rather than mathematics.

One focus of his mathematical work was Dirichlet series . In particular, he investigated, partly together with Edmund Landau , the Riemannian ζ-function , probably the best-known and most important Dirichlet series. In 1914 the two formulated Bohr-Landau's theorem , which - to put it simply - says that the majority of the zeros of the Riemann ζ-function lie in an arbitrarily small strip around the critical straight line. In addition, Bohr is the founder of the theory of near-periodic functions in a series of papers from 1924 to 1926 in Acta Mathematica. In the theory of the gamma function , he is one of the namesake for Bohr-Mollerup's theorem . Even the theorem that follows from for that for is now called Bohr's theorem (about power series). Bohr had actually only shown it in 1914 for the constant . That the sentence applies to and that it is the best possible was later independently proven by Marcel Riesz , Issai Schur and Friedrich Wilhelm Wiener . ${\ displaystyle \ left | \ sum _ {n = 0} ^ {\ infty} a_ {n} z ^ {n} \ right | \ leq 1}$ ${\ displaystyle | z | <1}$ ${\ displaystyle \ sum _ {n = 0} ^ {\ infty} \ left | a_ {n} z ^ {n} \ right | \ leq 1}$ ${\ displaystyle | z | \ leq {\ tfrac {1} {3}}}$ ${\ displaystyle {\ tfrac {1} {6}}}$ ${\ displaystyle {\ tfrac {1} {3}}}$ ${\ displaystyle {\ tfrac {1} {3}}}$

In 1915 Bohr became professor at the Polytechnic School in Copenhagen, and in 1930 he was appointed to the University of Copenhagen . From 1926 to 1951, interrupted only from 1930 to 1936, he was President of the Danish Mathematical Society (DMF). In 1925 he was elected a corresponding member of the Göttingen Academy of Sciences . Since 1926 he was a corresponding member of the Bavarian Academy of Sciences . In 1945 he was accepted into the American Philosophical Society .

In 1932 he gave a plenary lecture at the International Congress of Mathematicians in Zurich (almost periodic functions of a complex variable) and in 1950 he was invited speaker at the ICM in Cambridge (Massachusetts) (A survey of the different proofs of the main theorems in the theory of almost periodic functions ).

In 1934 an open letter from Ludwig Bieberbach to Bohr in the annual report of the German Mathematicians Association (DMV) caused a scandal that resulted in Bieberbach's resignation from his offices in the DMV. Bieberbach had published this letter, in which he responded to a criticism by Bohr (who had Jewish ancestors) of his mathematician typification, without voting in the annual report.

Fonts

Almost periodic functions . Berlin: Julius Springer, 1932 (English translation New York: Chelsea, 1947)

On the theory of almost periodic functions , 3 parts, Acta Mathematica, Volume 45, 1925, pp. 29-127, Volume 46, 1925, pp. 101-214, Volume 47, 1926, pp. 237-281

with Johannes Mollerup: Laerebog i matematisk analyze , 4 volumes, Copenhagen, 1915 to 1918 (last edition 1945 to 1949)

Erling Følner, Børge Jessen (eds.): Collected Mathematical Works of Harald Bohr , 3 volumes, Copenhagen: Dansk Matematisk Forening, 1950–1952.

Bohr “Almost Periodic Functions”, DMV Annual Report, Vol . 34, 1926 .

Bohr "The Riemann Zeta Function", DMV Annual Report Vol . 24, 1915 .

Bohr "About the uniform convergence of the Dirichletscher series", magazine for pure and applied mathematics, vol. 143, 1913 .

Bohr, Harald Cramér Recent Studies on Analytical Number Theory , Encyclopedia of Mathematical Sciences 1922 .

literature

Oskar Perron "Harald Bohr", DMV annual report 1952 .

Web links

Literature by and about Harald Bohr in the catalog of the German National Library .
Eric W. Weisstein: Bohr, Harald August (1887–1951) on ScienceWorld .
John J. O'Connor, Edmund F. Robertson : Harald August Bohr. In: MacTutor History of Mathematics archive . .
Harald Bohr in the database of Sports-Reference (English; archived from the original ).
Author profile in the database zbMATH
Harald Bohr on the official website of the Danish Football Association (Danish)

Remarks

↑ Harald Bohr in the Mathematics Genealogy Project (English)
↑ Bohr, Landau, A sentence on Dirichlet's series with application to the -function and the L-functions. Rend. Circ. Mat. Palermo, vol. 37, 1914, pp. 269-272 ${\ displaystyle \ zeta}$
^ A forerunner was the theory of quasi-periodic functions by Ernest Esclangon and Piers Bohl .
↑ Harald Bohr, Johannes Mollerup: Lærebog i matematisk Analyze III. (Copenhagen), Jul.Gjellerups Forlag, 1922
^ Bohr, A theorem concerning power series, Proc. London Math. Soc., Vol. 13, 1914, pp. 1-5
↑ Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 44.
↑ Member entry of Harald Bohr at the Bavarian Academy of Sciences , accessed on December 30, 2016.
↑ Member History: Harald Bohr. American Philosophical Society, accessed May 9, 2018 .
^ "The art of quoting, an open letter to Harald Bohr in Copenhagen", DMV annual report 1934
^ "New Mathematics" in Germany (Danish), May 1, 1934 in Berlingske Aften

personal data
SURNAME	Bohr, Harald
ALTERNATIVE NAMES	Bohr, Harald August (full name)
BRIEF DESCRIPTION	Danish mathematician and soccer player
DATE OF BIRTH	April 22, 1887
PLACE OF BIRTH	Copenhagen , Denmark
DATE OF DEATH	January 22, 1951
Place of death	Gentofte , Denmark

[1] Harald Bohr in the Mathematics Genealogy Project (English)

[2] Bohr, Landau, A sentence on Dirichlet's series with application to the -function and the L-functions. Rend. Circ. Mat. Palermo, vol. 37, 1914, pp. 269-272 ${\ displaystyle \ zeta}$

[3] A forerunner was the theory of quasi-periodic functions by Ernest Esclangon and Piers Bohl .

[4] Harald Bohr, Johannes Mollerup: Lærebog i matematisk Analyze III. (Copenhagen), Jul.Gjellerups Forlag, 1922

[5] Bohr, A theorem concerning power series, Proc. London Math. Soc., Vol. 13, 1914, pp. 1-5

[6] Holger Krahnke: The members of the Academy of Sciences in Göttingen 1751-2001 (= Treatises of the Academy of Sciences in Göttingen, Philological-Historical Class. Volume 3, Vol. 246 = Treatises of the Academy of Sciences in Göttingen, Mathematical-Physical Class. Episode 3, vol. 50). Vandenhoeck & Ruprecht, Göttingen 2001, ISBN 3-525-82516-1 , p. 44.

[7] Member entry of Harald Bohr at the Bavarian Academy of Sciences , accessed on December 30, 2016.

[8] Member History: Harald Bohr. American Philosophical Society, accessed May 9, 2018 .

[9] "The art of quoting, an open letter to Harald Bohr in Copenhagen", DMV annual report 1934

[10] "New Mathematics" in Germany (Danish), May 1, 1934 in Berlingske Aften