Albert Ingham

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

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.

References

1. 1 2 Albert Ingham at the Mathematics Genealogy Project
2. 1 2 3 O'Connor, John J.; Robertson, Edmund F., "Albert Ingham", MacTutor History of Mathematics archive, University of St Andrews .
3. ↑ 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. 
4. ↑ The Distribution of Prime Numbers, Cambridge University Press, 1932 (Reissued with a foreword by R. C. Vaughan in 1990)
5. ↑ Ingham, A. E. (1937). "On the Difference Between Consecutive Primes". The Quarterly Journal of Mathematics: 255. doi:10.1093/qmath/os-8.1.255.