“Albert Ingham”的意思、由来-开放百科全书

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Albert Ingham

释义

Education
Research
References

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|name = Albert Ingham
| birth_name = Albert Edward Ingham
|image =
|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 =
|doctoral_students = Wolfgang Fuchs
C. Haselgrove
Christopher Hooley
William Pennington
Robert Rankin^[1]
|notable_students =
|known_for =
|author_abbrev_bot =
|author_abbrev_zoo =
|influences = John Edensor Littlewood^[2]
|influenced =
|awards = Smith's Prize (1921)^[2]
Fellow of the Royal Society^[1]
|signature =
|footnotes = Erdős Number: 1
}}Albert Edward Ingham FRS (3 April 1900 – 6 September 1967) was an English mathematician.^[2]

Education

Ingham was born in Northampton. He went to Stafford Grammar School and Trinity College, Cambridge.^[3]

Research

Ingham supervised the Ph.D.s of C. Brian Haselgrove, Wolfgang Fuchs and Christopher Hooley.^[4] 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. ^{{Cite journal | last1 = Burkill | first1 = J. C. | doi = 10.1098/rsbm.1968.0012 | title = Albert Edward Ingham 1900-1967 | journal = Biographical Memoirs of Fellows of the Royal Society | volume = 14 | pages = 271–286| year = 1968 | pmid = | pmc = }}
2. ^The Distribution of Prime Numbers, Cambridge University Press, 1932 (Reissued with a foreword by R. C. Vaughan in 1990)
3. ^¹²{{MacTutor Biography|id=Ingham}}
4. ^¹{{MathGenealogy|id=30623}}
5. ^{{Cite journal | last1 = Ingham | first1 = A. E. | authorlink = Albert Ingham| title = On the Difference Between Consecutive Primes | doi = 10.1093/qmath/os-8.1.255 | journal = The Quarterly Journal of Mathematics | pages = 255 | year = 1937 | pmid = | pmc = }}

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