Albert Ingham
Albert Ingham | |
---|---|
Born | Albert Edward Ingham 3 April 1900 Northampton, Northamptonshire, England |
Died | 6 September 1967 Switzerland | (aged 67)
Alma mater | Trinity College, Cambridge |
Spouse(s) | |
Awards | Smith's Prize (1921) Fellow of the Royal Society |
Scientific career | |
Institutions | King's College, Cambridge |
Doctoral students | Wolfgang Fuchs C. Haselgrove Christopher Hooley Robert Rankin |
Influences | John Edensor Littlewood |
Notes | |
Erdős Number: 1 |
Albert Edward Ingham FRS (3 April 1900 – 6 September 1967) was an English mathematician.
Biography
Ingham was born in Northampton. He went to Stafford Grammar School and began his studies at Trinity College, Cambridge in January 1919 after service in the British Army in World War One. Ingham received a distinction as a Wrangler in the Mathematical Tripos at Cambridge. He was elected a fellow of Trinity in 1922. He also received an 1851 Research Fellowship.
Ingham married Rose Marie "Jane" Tupper‑Carey in 1932; the couple had two sons. Ingham died in Switzerland in 1967.
Research
Ingham was appointed a Reader at Leeds University in 1926 and returned to Cambridge University as a fellow of King's College and lecturer in 1930. Ingham was appointed after the death of Frank Ramsey. Ingham was elected a Fellow of the Royal Society in 1945. Ingham's sole book, On the Distribution of Prime Numbers was published in 1932.
Ingham supervised the Ph.D.s of C. Brian Haselgrove, Wolfgang Fuchs and Christopher Hooley.
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
- gn < pn5/8,
where pn the n-th prime number and gn = pn+1 − pn denotes the n-th prime gap.
- 1900 births
- 1967 deaths
- 20th-century English non-fiction writers
- 20th-century mathematicians
- Academics of the University of Leeds
- Alumni of Trinity College, Cambridge
- British Army personnel of World War I
- English mathematicians
- Fellows of King's College, Cambridge
- Fellows of Trinity College, Cambridge
- Fellows of the Royal Society
- Number theorists
- People educated at Salford Grammar School
- People from Northampton