Hugh Lowell Montgomery (born August 26, 1944) is an

American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the "United States" or "America" ** Americans, citizens and nationals of the United States of America ** American ancestry, pe ...

mathematician, working in the fields of

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diric ...

and

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

. As a

Marshall scholar The Marshall Scholarship is a postgraduate scholarship for "intellectually distinguished young Americans ndtheir country's future leaders" to study at any university in the United Kingdom. It is widely considered one of the most prestigious sc ...

, Montgomery earned his Ph.D. from the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. For many years, Montgomery has been teaching at the

University of Michigan , mottoeng = "Arts, Knowledge, Truth" , former_names = Catholepistemiad, or University of Michigania (1817–1821) , budget = $10.3 billion (2021) , endowment = $17 billion (2021)As o ...

. He is best known for

Montgomery's pair correlation conjecture In mathematics, Montgomery's pair correlation conjecture is a conjecture made by that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is :1-\left(\frac\right)^ + \delta(u), which ...

, his development of the

large sieve method The large sieve is a method (or family of methods and related ideas) in analytic number theory. It is a type of sieve where up to half of all residue classes of numbers are removed, as opposed to small sieves such as the Selberg sieve wherein onl ...

s and for co-authoring (with

Ivan M. Niven Ivan Morton Niven (October 25, 1915 May 9, 1999) was a Canadian-American mathematician, specializing in number theory and known for his work on Waring's problem. He worked for many years as a professor at the University of Oregon, and was presiden ...

and

Herbert Zuckerman Herbert may refer to: People Individuals * Herbert (musician), a pseudonym of Matthew Herbert Name * Herbert (given name) * Herbert (surname) Places Antarctica * Herbert Mountains, Coats Land * Herbert Sound, Graham Land Australia * Herbert, ...

) one of the standard introductory number theory texts, ''An Introduction to the Theory of Numbers'', now in its fifth edition (). In 1974 Montgomery was an invited speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

(ICM) in Vancouver. In 2012 he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Bibliography

* * Davenport, Harold. ''Multiplicative number theory''. Third edition. Revised and with a preface by Hugh L. Montgomery. Graduate Texts in Mathematics, 74. Springer-Verlag, New York, 2000. xiv+177 pp. . * Levinson, Norman; Montgomery, Hugh L
"Zeros of the derivatives of the Riemann zeta function"
''Acta Mathematica'' 133 (1974), 49–65. * Montgomery, Hugh L
''Topics in multiplicative number theory''
Lecture Notes in Mathematics, Vol. 227. Springer-Verlag, Berlin-New York, 1971. ix+178 pp. * Montgomery, Hugh L
''Ten lectures on the interface between analytic number theory and harmonic analysis''
CBMS Regional Conference Series in Mathematics, 84. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1994. xiv+220 pp. . * Montgomery, H. L.; Vaughan, R. C. The large sieve. Mathematika 20 (1973), 119–134. * Montgomery, Hugh L., and Vaughan, Robert C
''Multiplicative number theory. I. Classical theory''
Cambridge Studies in Advanced Mathematics, 97. Cambridge University Press, Cambridge, 2006. xviii+552 pp. ; 0-521-84903-9. * Niven, Ivan; Zuckerman, Herbert S.; Montgomery, Hugh L. ''An introduction to the theory of numbers''. Fifth edition. John Wiley & Sons, Inc., New York, 1991. xiv+529 pp. *

References

External links

Number theorists Alumni of the University of Cambridge 20th-century American mathematicians 21st-century American mathematicians University of Michigan faculty American Rhodes Scholars 1944 births Living people Fellows of the American Mathematical Society {{US-mathematician-stub