Albert Ingham - Alchetron, The Free Social Encyclopedia

Name Albert Ingham Role Mathematician
Born Albert Edward Ingham3 April 1900Northampton ( 1900-04-03 ) Institutions University of Cambridge Alma mater Trinity College, Cambridge Doctoral students Wolfgang FuchsC. HaselgroveChristopher HooleyWilliam PenningtonRobert Rankin Influences John Edensor Littlewood Notable awards Smith's Prize (1921)Fellow of the Royal Society Died September 6, 1967, Chamonix, France Books The distribution of prime numbers, Hydrography for the surveyor and engineer Education Trinity College, Cambridge, University of Cambridge People also search for John Edensor Littlewood Notable students Robert Alexander Rankin, Christopher Hooley, Wolfgang Heinrich Johannes Fuchs, C. Brian Haselgrove
Influenced by John Edensor Littlewood

Albert Edward Ingham FRS (3 April 1900 – 6 September 1967) was an English mathematician.

Education

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

ζ ( 1 / 2 + i t ) = O ( t c )

for some positive constant c, then

π ( x + x θ ) − π ( x ) ∼ x θ 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

g_n < p_n^5/8,

where p_n the n-th prime number and g_n = p_n+1 − p_n denotes the n-th prime gap.

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