Albert Ingham

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Quick facts

Intro

English mathematician

Gender:

Male

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Birth:

3 April 1900(Northampton, Northampton, Northamptonshire, East Midlands)

Death:

6 September 1967(Chamonix-Mont-Blanc, canton of Chamonix-Mont-Blanc, arrondissement of Bonneville, Haute-Savoie)

The details

Biography

Introduction

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