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{{Use dmy dates|date=May 2012}} | |||
{{Use British English|date=May 2012}} | |||
{{Infobox scientist | |||
|name = Albert Ingham | |||
| birth_name = Albert Edward Ingham | |||
|image = <!--(filename only)--> | |||
|image_size = | |||
|caption = | |||
|birth_date = {{birth date|1900|4|3|df=y}} | |||
|birth_place = [[Northampton]] | |||
|death_date = {{death date and age|1967|9|6|1900|4|3|df=y}} | |||
|death_place = | |||
|residence = | |||
|citizenship = | |||
|nationality = | |||
|ethnicity = | |||
|fields = | |||
|workplaces = [[University of Cambridge]] | |||
|alma_mater =[[Trinity College, Cambridge]] | |||
|academic_advisors = | |||
|doctoral_advisor = <!-- No advisor as Ingham didn't do a PhD. See talk page --> | |||
|doctoral_students = [[Wolfgang Heinrich Johannes Fuchs|Wolfgang Fuchs]]<br />[[C. Brian Haselgrove|C. Haselgrove]]<br />[[Christopher Hooley]]<br />William Pennington<br />[[Robert Alexander Rankin|Robert Rankin]]<ref name="mathgene"/> | |||
|notable_students = | |||
|known_for = | |||
|author_abbrev_bot = | |||
|author_abbrev_zoo = | |||
|influences = [[John Edensor Littlewood]]<ref name="mactutor" /> | |||
|influenced = | |||
|awards = [[Smith's Prize]] (1921)<ref name="mactutor" /><br>[[Fellow of the Royal Society]]<ref name="frs">{{cite doi|10.1098/rsbm.1968.0012}}</ref> | |||
|signature = <!--(filename only)--> | |||
|footnotes = Erdős Number: 1 | |||
}} | |||
'''Albert Edward Ingham''' [[Fellow of the Royal Society|FRS]] (3 April 1900 – 6 September 1967) was an [[England|English]] [[mathematician]].<ref>''The Distribution of Prime Numbers'', Cambridge University Press, 1934 (Reissued with a foreword by [[Robert Charles Vaughan (mathematician)|R. C. Vaughan]] in 1990)</ref> | |||
==Education== | |||
Ingham was born in [[Northampton]]. He went to Stafford Grammar School and [[Trinity College, Cambridge]].<ref name="mactutor">{{MacTutor Biography|id=Ingham}}</ref> | |||
==Research== | |||
Ingham supervised the Ph.D.s of [[C. Brian Haselgrove]], [[Wolfgang Heinrich Johannes Fuchs|Wolfgang Fuchs]] and [[Christopher Hooley]].<ref name="mathgene">{{MathGenealogy|id=30623}}</ref> Ingham died in [[Chamonix]], [[France]]. | |||
Ingham proved in 1937<ref>{{cite doi|10.1093/qmath/os-8.1.255}}</ref> that if | |||
:<math>\zeta\left(1/2+it\right)\in O\left(t^c\right)</math> | |||
for some positive constant ''c'', then | |||
:<math>\pi\left(x+x^\theta\right)-\pi(x)\sim\frac{x^\theta}{\log x},</math> | |||
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''<sub>''n''</sub> < ''p''<sub>''n''</sub><sup>5/8</sup>, | |||
where ''p''<sub>''n''</sub> the ''n''-th [[prime number]] and ''g''<sub>''n''</sub> = ''p''<sub>''n''+1</sub> − ''p''<sub>''n''</sub> denotes the ''n''-th [[prime gap]]. | |||
==References== | |||
<references/> | |||
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. --> | |||
| NAME =Ingham, Albert | |||
| ALTERNATIVE NAMES = | |||
| SHORT DESCRIPTION = British mathematician | |||
| DATE OF BIRTH =3 April 1900 | |||
| PLACE OF BIRTH =[[Northampton]] | |||
| DATE OF DEATH =6 September 1967 | |||
| PLACE OF DEATH = | |||
}} | |||
{{DEFAULTSORT:Ingham, Albert}} | |||
[[Category:1900 births]] | |||
[[Category:1967 deaths]] | |||
[[Category:People from Northampton]] | |||
[[Category:20th-century mathematicians]] | |||
[[Category:Number theorists]] | |||
[[Category:Alumni of Trinity College, Cambridge]] | |||
[[Category:Fellows of the Royal Society]] | |||
[[Category:English mathematicians]] | |||
{{England-scientist-stub}} | |||
{{UK-mathematician-stub}} | |||
Revision as of 21:00, 17 August 2013
30 year-old Entertainer or Range Artist Wesley from Drumheller, really loves vehicle, property developers properties for sale in singapore singapore and horse racing. Finds inspiration by traveling to Works of Antoni Gaudí. Template:Use British English Template:Infobox scientist Albert Edward Ingham FRS (3 April 1900 – 6 September 1967) was an English mathematician.[1]
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.[3] Ingham died in Chamonix, France.
Ingham proved in 1937[4] 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.
References
- ↑ The Distribution of Prime Numbers, Cambridge University Press, 1934 (Reissued with a foreword by R. C. Vaughan in 1990)
- ↑ Template:MacTutor Biography
- ↑ 50 yr old Print Journalist Broadbent from Deep River, has hobbies and interests which includes r/c helicopters, property developers in singapore house for rent and scrabble. Suggests that you go to Tomb of Askia.
- ↑ Template:Cite doi
Template:England-scientist-stub Template:UK-mathematician-stub