Hugh Montgomery (mathematician)


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 The United States of America (USA), commonly known as the United States (U.S. or US), or America, is ...
mathematician, working in the fields of
analytic number theory In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and t ...
mathematical analysis Analysis is the branch of mathematics dealing with Limit (mathematics), limits and related theories, such as Derivative, differentiation, Integral, integration, Measure (mathematics), measure, sequences, Series (mathematics), series, and analytic ...
. As a
Marshall scholar The Marshall Scholarship is a Postgraduate student, postgraduate scholarship for "intellectually distinguished young Americans their country's future leaders" to study at any university in the United Kingdom. It is widely considered one o ...
, 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 Scholars of ...
. 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 = $8.99 billion (2018) , endowment = $17 billion (2021)As of October 25, 2021. ...

University of Michigan
. He is best known for Montgomery's pair correlation conjecture, his development of the
large sieve method The large sieve is a method (or family of methods and related ideas) in analytic number theory 300px, Riemann zeta function ''ζ''(''s'') in the complex plane. The color of a point ''s'' encodes the value of ''ζ''(''s''): colors close to black deno ...
s and for co-authoring (with
Ivan M. Niven Ivan Morton Niven (October 25, 1915 May 9, 1999) was a Canadian Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or al ...
and Herbert Zuckerman) 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 mathematics, mathematical research and scholarship, and serves the national and international community through its publicatio ...


* *
Davenport, Harold
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 Math.'' 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. *


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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 Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death mi ...
Fellows of the American Mathematical Society {{US-mathematician-stub