| Albert Edward Ingham | |
|---|---|
| Born | 3 April 1900 Northampton |
| Died | 6 September 1967 (aged 67) |
| Alma mater | University of Cambridge |
| Doctoral advisor | John Littlewood |
| Doctoral students | Wolfgang Fuchs C. Haselgrove Christopher Hooley William Pennington Robert Rankin |
|
Notes
Erdős Number: 1 |
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Albert Edward Ingham (3 April 1900 – 6 September 1967) was an English mathematician.
Ingham was born in Northampton. He went to Stafford Grammar School and Trinity College, Cambridge [1]. He obtained his Ph.D., which was supervised by John Edensor Littlewood, from the University of Cambridge. He supervised the Ph.D.s of C. Brian Haselgrove, Wolfgang Fuchs and Christopher Hooley.[2] Ingham died in Chamonix, France.
Ingham proved in 1937[3] that if
- Failed to parse (Missing texvc executable; please see math/README to configure.): \zeta\left(1/2+it\right)\in O\left(t^c\right)
for some positive constant c, then
- Failed to parse (Missing texvc executable; please see math/README to configure.): \pi\left(x+x^\theta\right)-\pi(x)\sim\frac{x^\theta}{\log x},
for any θ > (1+4c)/(2+4c). Here ζ denotes the Riemann zeta function and π the prime-counting function.
Using the best published value for c at the time, an immediate consequence of his result was that
- gn < pn5/8,
where pn the n-th prime number and gn = pn+1 − pn denotes the n-th prime gap.
Books [link]
- The Distribution of Prime Numbers, Cambridge University Press, 1934 (Reissued with a foreword by R. C. Vaughan in 1990)
References [link]
- ^ https://www.gap-system.org/~history/Biographies/Ingham.html
- ^ Albert Ingham at the Mathematics Genealogy Project
- ^ Ingham, A. E. On the difference between consecutive primes, Quarterly Journal of Mathematics (Oxford Series), 8, pages 255–266, (1937)
External links [link]
- O'Connor, John J.; Robertson, Edmund F., "Albert Ingham", MacTutor History of Mathematics archive, University of St Andrews, https://www-history.mcs.st-andrews.ac.uk/Biographies/Ingham.html.
- Albert Ingham at the Mathematics Genealogy Project
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