Department of Mathematics

Breadcrumb

Michael Rosen

Professor Emeritus/Adjunct
michael_rosen@brown.edu
Research Interests Algebraic Number Theory, The arithmetic of algebraic function fields, Arithmetic algebraic geometry

Biography

Mailing Address

Mathematics Department
Box 1917
Brown University
Providence, RI 02912

Background

Education: Ph.D., Princeton, 1963

Publications

  • Hermite's Theorem for Function Fields, Submitted for publication to Acta Arithmetica, May, 2013. w/ S. Wong.
  • Class Groups in Cyclic  extensions: Comments on a Paper by G. Cornell, Accepted for publication in the Proceedings of the A.M.S.
  • David Hayes; Some remarks on his Life and Work, Journal of Number Theory, 133 (2013) , 825-829.
  • Polynomials mod p and the Theory of Galois Sets, Theory and Applications of Finite Fields, 163-178. Cont. Math., 579, Amer. Math Society, Providence, RI, 2012.
  • Prime decompositions in infinite extensions of global fields, Communications in Algebra 40, (2012), no. 4, 1260-1267, w/ D. Dobbs
  • Function Fields With Class Number Indivisible by a Prime , Acta Arithmetica, 150, (2011), no. 4, 339-359.w/ J. Daub, J. Lang, M. Merling, A. Pacelli, and N. Pitiwan.
  • Indivisibility of Class Numbers of Global Function Fields, Acta Arithmetica 138.3, (2009), pp. 269-287. w/ A. Pacelli.
  • Formal Drinfeld Modules. Journal of Number Theory 103 (2003), pp. 234-256.
  • Number theory in function fields. Graduate Texts in Mathematics 210 . Springer-Verlag, New York, 2002. xii+358 pp. ISBN: 0-387-95335-3
  • The rank of abelian varieties over infinite Galois extensions. J. Number Theory 92 (2002), no. 1, 182--196. w/ Wong, Simon
  • Average rank for elliptic curves and a conjecture of Nagao. Applications of curves over finite fields (Seattle, WA, 1997), 221--226, Contemp. Math., 245, Amer. Math. Soc., Providence, RI, 1999. 
  • A generalization of Mertens' theorem. J. Ramanujan Math. Soc. 14 (1999), no. 1, 1--19. 
  • On the rank of an elliptic surface. Invent. Math. 133 (1998), no. 1, 43--67. w/Silverman, Joseph H.
  • Remarks on the history of Fermat's last theorem 1844 to 1984. Modular forms and Fermat's last theorem (Boston, MA, 1995), 505--525, Springer, New York, 1997. 
  • A note on the relative class number in function fields. Proc. Amer. Math. Soc. 125 (1997), no. 5, 1299--1303. 
  • Variations on a theme of Romanoff. Internat. J. Math. 7 (1996), no. 3, 373--391. w/Murty, M. Ram; Silverman, Joseph H.
  • Average value of class numbers in cyclic extensions of the rational function field. Number theory (Halifax, NS, 1994), 307--323, CMS Conf. Proc., 15, Amer. Math. Soc., Providence, RI, 1995. 
  • Average value of K2({\scr O})\vert  in function fields. Special issue dedicated to Leonard Carlitz. Finite Fields Appl. 1 (1995), no. 2, 235--241. 
  • Niels Hendrik Abel and equations of the fifth degree. Amer. Math. Monthly 102 (1995), no. 6, 495--505. 
  • Idempotent relations among arithmetic invariants attached to number fields and algebraic varieties. J. Number Theory 46 (1994), no. 2, 230--254. w/Kani, Ernst

Awards

Former Ph.D. Students

  • Allan Rosenberg 1969
  • Steve Tillman 1970
  • Steven Galovich 1972
  • Robert Bond 1973
  • Stuart Zamlong 1977
  • Gary Cornell 1978 
  • Constantine Spyropoulos 1984
  • Jesse Deutsch 1986
  • Margaret Napolitano 1986
  • David Solomon 1988
  • Chris Friesen 1989
  • Linghsueh Shu 1992
  • James Sauerberg 1993
  • Hua Chi Li 1994
  • Chao Qun Li 1996
  • Gisele Menochi 1996 
  • Joshua Holden 1998
  • Yoonjin Lee 1999
  • Michael Reid 2000
  • Allison Pacelli 2003