Albert Ingham
Albert Ingham | |
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Born |
Albert Edward Ingham 3 April 1900 Northampton |
Died | 6 September 1967 67) | (aged
Institutions | University of Cambridge |
Alma mater | Trinity College, Cambridge |
Doctoral students |
Wolfgang Fuchs C. Haselgrove Christopher Hooley William Pennington Robert Rankin[1] |
Influences | John Edensor Littlewood[2] |
Notable awards |
Smith's Prize (1921)[2] Fellow of the Royal Society[3] |
Notes | |
Erdős Number: 1 |
Albert Edward Ingham FRS (3 April 1900 – 6 September 1967) was an English mathematician.[4]
Education
Ingham was born in Northampton. He went to Stafford Grammar School and Trinity College, Cambridge.[2]
Research
Ingham supervised the Ph.D.s of C. Brian Haselgrove, Wolfgang Fuchs and Christopher Hooley.[1] Ingham died in Chamonix, France.
Ingham proved in 1937[5] that if
for some positive constant c, then
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.
References
- 1 2 Albert Ingham at the Mathematics Genealogy Project
- 1 2 3 O'Connor, John J.; Robertson, Edmund F., "Albert Ingham", MacTutor History of Mathematics archive, University of St Andrews.
- ↑ Burkill, J. C. (1968). "Albert Edward Ingham 1900-1967". Biographical Memoirs of Fellows of the Royal Society 14: 271–226. doi:10.1098/rsbm.1968.0012.
- ↑ The Distribution of Prime Numbers, Cambridge University Press, 1932 (Reissued with a foreword by R. C. Vaughan in 1990)
- ↑ Ingham, A. E. (1937). "On the Difference Between Consecutive Primes". The Quarterly Journal of Mathematics: 255. doi:10.1093/qmath/os-8.1.255.
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