# Edmund Landau

Last updated
Edmund Landau
Born
Edmund Georg Hermann Landau

14 February 1877
Died19 February 1938 (aged 61)
Berlin, Germany
NationalityGerman
Alma mater University of Berlin
Known for Distribution of prime numbers
Landau prime ideal theorem
Spouse(s)Marianne Ehrlich
Scientific career
Fields Number theory
Complex analysis
Institutions University of Berlin
University of Göttingen
Hebrew University of Jerusalem
Lazarus Fuchs
Doctoral students Binyamin Amirà
Paul Bernays
Harald Bohr
Gustav Doetsch
Hans Heilbronn
Grete Hermann
Dunham Jackson
Erich Kamke
Aubrey Kempner
Alexander Ostrowski
Carl Ludwig Siegel
Arnold Walfisz
Vojtěch Jarník

Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis.

## Biography

Edmund Landau was born to a Jewish family in Berlin. His father was Leopold Landau, a gynecologist and his mother was Johanna Jacoby. Landau studied mathematics at the University of Berlin, receiving his doctorate in 1899 and his habilitation (the post-doctoral qualification required to teach in German universities) in 1901. His doctoral thesis was 14 pages long.

In 1895, his paper on scoring chess tournaments is the earliest use of eigenvector centrality. [1] [2]

Landau taught at the University of Berlin from 1899 to 1909, after which he held a chair at the University of Göttingen. He married Marianne Ehrlich, the daughter of the Nobel Prize-winning biologist Paul Ehrlich, in 1905.

At the 1912 International Congress of Mathematicians Landau listed four problems in number theory about primes that he said were particularly hard using current mathematical methods. They remain unsolved to this day and are now known as Landau's problems.

During the 1920s, Landau was instrumental in establishing the Mathematics Institute at the nascent Hebrew University of Jerusalem. Intent on eventually settling in Jerusalem, he taught himself Hebrew and delivered a lecture entitled Solved and unsolved problems in elementary number theory in Hebrew on 2 April 1925 during the University's groundbreaking ceremonies. He negotiated with the University's president, Judah Magnes, regarding a position at the University and the building that was to house the Mathematics Institute.

Landau and his family emigrated to Mandatory Palestine in 1927 and he began teaching at the Hebrew University. The family had difficulty adjusting to the primitive living standards then available in Jerusalem. In addition, Landau became a pawn in a struggle for control of the University between Magnes and Chaim Weizmann and Albert Einstein. Magnes suggested that Landau be appointed Rector of the University, but Einstein and Weizmann supported Selig Brodetsky. Landau was disgusted by the dispute and decided to return to Göttingen, remaining there until he was forced out by the Nazi regime after the Machtergreifung in 1933. Thereafter, he lectured only outside Germany. He moved to Berlin in 1934, where he died in early 1938 of natural causes.

In 1903, Landau gave a much simpler proof than was then known of the prime number theorem and later presented the first systematic treatment of analytic number theory in the Handbuch der Lehre von der Verteilung der Primzahlen (the "Handbuch"). [3] He also made important contributions to complex analysis.

G. H. Hardy wrote that no one was ever more passionately devoted to mathematics than Landau.[ citation needed ]

## Translated works

• Foundations of Analysis, Chelsea Pub Co. ISBN   0-8218-2693-X.
• Differential and Integral Calculus, American Mathematical Society. ISBN   0-8218-2830-4.
• Elementary Number Theory, American Mathematical Society. ISBN   0-8218-2004-4.

## Related Research Articles

Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity. Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation.

Paul Julius Oswald Teichmüller was a German mathematician who made contributions to complex analysis. He introduced quasiconformal mappings and differential geometric methods into the study of Riemann surfaces. Teichmüller spaces are named after him.

Ernst Friedrich Ferdinand Zermelo was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.

In number theory, a natural number is called k-almost prime if it has k prime factors. More formally, a number n is k-almost prime if and only if Ω(n) = k, where Ω(n) is the total number of primes in the prime factorization of n :

Ferdinand Georg Frobenius was a German mathematician, best known for his contributions to the theory of elliptic functions, differential equations, number theory, and to group theory. He is known for the famous determinantal identities, known as Frobenius–Stickelberger formulae, governing elliptic functions, and for developing the theory of biquadratic forms. He was also the first to introduce the notion of rational approximations of functions, and gave the first full proof for the Cayley–Hamilton theorem. He also lent his name to certain differential-geometric objects in modern mathematical physics, known as Frobenius manifolds.

Legendre's constant is a mathematical constant occurring in a formula conjectured by Adrien-Marie Legendre to capture the asymptotic behavior of the prime-counting function . Its value is now known to be 1.

Abraham Fraenkel was a German-born Israeli mathematician. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his additions to Ernst Zermelo's axioms, which resulted in the Zermelo–Fraenkel set theory.

Vorlesungen über Zahlentheorie is the name of several different textbooks of number theory. The best known was written by Peter Gustav Lejeune Dirichlet and Richard Dedekind, and published in 1863. Others were written by Leopold Kronecker, Edmund Landau, and Helmut Hasse. They all cover elementary number theory, Dirichlet's theorem, quadratic fields and forms, and sometimes more advanced topics.

Ilya Piatetski-Shapiro was a Soviet-born Israeli mathematician. During a career that spanned 60 years he made major contributions to applied science as well as pure mathematics. In his last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions.

Isaac Jacob Schoenberg was a Romanian-American mathematician, known for his invention of splines.

In number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens. "Mertens' theorem" may also refer to his theorem in analysis.

Heinrich Franz Friedrich Tietze was an Austrian mathematician, famous for the Tietze extension theorem on functions from topological spaces to the real numbers. He also developed the Tietze transformations for group presentations, and was the first to pose the group isomorphism problem. Tietze's graph is also named after him; it describes the boundaries of a subdivision of the Möbius strip into six mutually-adjacent regions, found by Tietze as part of an extension of the four color theorem to non-orientable surfaces.

Georg Karl Wilhelm Hamel was a German mathematician with interests in mechanics, the foundations of mathematics and function theory.

Judah Leon Magnes was a prominent Reform rabbi in both the United States and Mandatory Palestine. He is best remembered as a leader in the pacifist movement of the World War I period, his advocacy of a binational Jewish-Arab state in Palestine, and as one of the most widely recognized voices of 20th century American Reform Judaism. Magnes served as the first chancellor of the Hebrew University of Jerusalem (1925), and later as its President (1935–1948).

Heinrich Martin Weber was a German mathematician. Weber's main work was in algebra, number theory, and analysis. He is best known for his text Lehrbuch der Algebra published in 1895 and much of it is his original research in algebra and number theory. His work Theorie der algebraischen Functionen einer Veränderlichen established an algebraic foundation for Riemann surfaces, allowing a purely algebraic formulation of the Riemann-Roch theorem. Weber's research papers were numerous, most of them appearing in Crelle's Journal or Mathematische Annalen. He was the editor of Riemann's collected works.

In mathematics, the Riemann Xi function is a variant of the Riemann zeta function, and is defined so as to have a particularly simple functional equation. The function is named in honour of Bernhard Riemann.

Paul Gustav Samuel Stäckel was a German mathematician, active in the areas of differential geometry, number theory, and non-Euclidean geometry. In the area of prime number theory, he used the term twin prime for the first time.

Paul Trevier Bateman was an American number theorist, known for formulating the Bateman–Horn conjecture on the density of prime number values generated by systems of polynomials and the New Mersenne conjecture relating the occurrences of Mersenne primes and Wagstaff primes.

The Einstein Institute of Mathematics is a centre for scientific research in mathematics at the Hebrew University of Jerusalem, founded in 1925 with the opening of the University. A leading research institute, the institute's faculty has included recipients of the Nobel Prize, Fields Medal, Wolf Prize, and Israel Prize.

Binyamin A. Amirà was an Israeli mathematician.

## References

1. Endmund Landau (1895). "Zur relativen Wertbemessung der Turnierresultate". Deutsches Wochenschach (11): 366–369. doi:10.1007/978-1-4615-4819-5_23.
2. Holme, Peter (15 April 2019). "Firsts in network science" . Retrieved 17 April 2019.
3. Gronwall, T. H. (1914). "Review: Handbuch der Lehre von der Verteilung der Primzahlen". Bull. Amer. Math. Soc. 20 (7): 368–376. doi:.