Albert Ingham

Albert Edward Ingham (born April 3, 1900 in Northampton , † September 6, 1967 in Chamonix ) was an English mathematician who dealt with analytical number theory and analysis .

Life

Ingham attended Trinity College at Cambridge University on a scholarship from 1919 (after a few months as a soldier in the First World War). He excelled in the Mathematical Tripos and won the Smith Prize . In 1922 he was elected a Fellow of Trinity College. In the same year he received his doctorate with John Edensor Littlewood . He then devoted himself exclusively to research for a few years and also attended the University of Göttingen . In 1926 he became a reader at Leeds University . From 1930 he was back in Cambridge as a lecturer. In 1953 he became a reader. He died while on a hiking holiday in the Alps.

Ingham dealt with analytical number theory, especially the theory of the Riemannian zeta function and the prime number distribution (about which he wrote a classic textbook in 1932), but also the series theory and Taubers ( following Norbert Wiener ). In 1937 he tightened Guido Hoheisel's estimate of the difference between successive prime numbers. In 1919 he gave a method how to find a counterexample for a conjecture by Pólya , with which RS Lehman finally found a counterexample with the help of a computer in 1960.

In 1945 he was admitted to the Royal Society .

Colin Brian Haselgrove is one of his PhD students .

Fonts

On the distribution of prime numbers. Cambridge University Press (Cambridge Tracts), 1932.

Web links

• John J. O'Connor, Edmund F. Robertson :  Albert Ingham. In: MacTutor History of Mathematics archive .

Individual evidence

1. ↑ Let , where denotes the number of prime factors of (with multiples). Pólya guessed for everyone . ${\displaystyle \lambda (n):=(-1)^{s}}$ ${\displaystyle s}$ ${\displaystyle n}$ ${\displaystyle \sum _{n=1}^{N}\lambda (n)\leq 0}$ ${\displaystyle N\in \mathbb {N} }$