Albert Ingham
Albert Ingham | |
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Born | Albert Edward Ingham 3 April 1900 Northampton |
Died | Script error: The function "death_date_and_age" does not exist. |
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
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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
- ↑ 1.0 1.1 Albert Ingham at the Mathematics Genealogy Project
- ↑ 2.0 2.1 2.2 Lua error in package.lua at line 80: module 'strict' not found..
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- ↑ The Distribution of Prime Numbers, Cambridge University Press, 1932 (Reissued with a foreword by R. C. Vaughan in 1990)
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
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