Michael Rosen

Professor Emeritus

Email: mrosen<at>math.brown.edu

 

Mailing Address:

Mathematics Department
Box 1917
Brown University
Providence, RI 02912

 

RESEARCH INTERESTS - Algebraic number theory, the arithmetic of algebraic function fields, arithmetic algebraic geometry

BACKGROUND - Education: Ph.D., Princeton, 1963

RECENT PUBLICATION

  • 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

FORMER PhD 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