Albert Ingham
| Albert Ingham | |
|---|---|
| Born | Albert Edward Ingham 3 April 1900 Northampton |
| Died | 6 September 1967 (aged 67) |
| Institutions | University of Cambridge |
| Alma mater | Trinity College, Cambridge |
| Doctoral students |
Wolfgang Fuchs C. Haselgrove Christopher Hooley William Pennington Robert Rankin |
| Influences | John Edensor Littlewood |
| Notable awards |
Smith's Prize (1921) Fellow of the Royal Society |
| Notes | |
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Erdős Number: 1
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Albert Edward Ingham FRS (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.
Ingham supervised the Ph.D.s of C. Brian Haselgrove, Wolfgang Fuchs and Christopher Hooley. Ingham died in Chamonix, France.
Ingham proved in 1937 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
where pn the n-th prime number and gn = pn+1 − pn denotes the n-th prime gap.
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