Albert Ingham

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

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

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.

Books

• The Distribution of Prime Numbers, Cambridge University Press, 1934 (Reissued with a foreword by R. C. Vaughan in 1990)

References

1. ^ http://www.gap-system.org/~history/Biographies/Ingham.html
2. ^ Albert Ingham at the Mathematics Genealogy Project
3. ^ Ingham, A. E. On the difference between consecutive primes, Quarterly Journal of Mathematics (Oxford Series), 8, pages 255–266, (1937)

External links

• O'Connor, John J.; Robertson, Edmund F., "Albert Ingham", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Ingham.html .
• Albert Ingham at the Mathematics Genealogy Project

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