Robert Rumely

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Robert Scott Rumely (born June 23, 1952 in Pullman (Washington) ) is an American mathematician who deals with number theory.


Rumely studied at Grinnel College in Iowa ( Bachelor 1974) and received his doctorate in 1978 from Princeton University under Gorō Shimura ( An Explicit Formula for the Grössencharacter of an Abelian Variety with Complex Multiplication ). From 1978 he was Moore Instructor at the Massachusetts Institute of Technology and 1980/81 at Harvard University . From 1981 he was Assistant Professor, from 1985 Associate Professor and from 1990 Professor at the University of Georgia . He has been visiting scholar and visiting professor at Macquarie University , the University of Michigan , Brown University , the Tata Institute of Fundamental Research (1985), IHES (1985), MSRI (1987), University of Bordeaux (1998), from the University of Paris VI and at the Institut Henri Poincaré (1999).

With Leonard Adleman and Carl Pomerance , he published the APR primality test (improved by Hendrik Lenstra and Henri Cohen and therefore also called the APRCL test).

He dealt with arithmetic algebraic geometry (for example the concept of capacity on algebraic curves, which David Cantor also introduced in 1980 as an extension of the concept of the transfinite diameter), arithmetic (p-adic) dynamics (partly with Matthew Baker ), applications of mathematical logic in arithmetic , algebraic number theory. For example, in 1986 he showed that in contrast to the integers in the ring of algebraic integers, there is an algorithm for Hilbert's tenth problem.

From 1984 to 1987 he was a Sloan Research Fellow .


  • Capacity theory on algebraic curves (Lecture Notes in Mathematics; Vol. 1378). Springer, Berlin 1989, ISBN 3-540-51410-4 .
  • Existence of the sectional capacity (Memoirs of the AMS; Vol. 145). American Mathematical Society, Providence, RI 2000, ISBN 0-8218-2058-3 (with Chi F. Lau and Robert Varley).
  • Arithmetic over the ring of all algebraic integers , J. Reine Angew. Math., Vol. 368, 1966, pp. 127-133


  • B. Green, F. Pop, Peter Roquette On Rumely's local global principle , Annual Report DMV, Volume 97, 1995, Issue 2

Web links


  1. ^ Adleman, Pomerance, Rumely: On distinguishing prime numbers from composites , Annals of Mathematics, Vol. 117, 1983, p. 173. Also Rumely: Recent advances in primality testing , Notices AMS, August 1983
  2. Rumely: Undecidability and definability in the theory of global fields . Transactions AMS Vol. 262, 1981, pp. 195-217, Arithmetic over the ring of all algebraic integers . Journal für Reine und Angewandte Mathematik, Vol. 368, 1986, pp. 127-133.