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Faculty Member

Michael Rosen

Professor of Mathematics

CONTACT INFO

Office: 112 Kassar-Gould House
Phone: (401) 863-2592
Fax: (401) 863-9013
Email: mrosen<at>math.brown.edu
Email: michael_rosen<at>brown.edu

Mailing Address:

    Mathematics Department
    Box 1917
    Brown University
    Providence, RI 02912

COURSE SCHEDULE

Spring 2013

Math 1540: Topics in Abstract Algebra

RESEARCH INTERESTS

Algebraic number theory
The arithmetic of algebraic function fields, arithmetic algebraic geometry

BACKGROUND

Education: Ph.D., Princeton, 1963; B.A., Brandeis, 1959

PUBLICATIONS 1994 - PRESENT

The P-rank of the Class Group in Cyclic P-power Extensions, Submitted for publication (available in PDF).

Primes in Infinite Extensions of Number Fields, Accepted for publication by Communications in Algebra, 2010. w/ D. Dobbs

Function Fields With Class Number Indivisible by a Prime , Accepted for publication by Acta Arithmetica, 2010. 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 $\vert K\sb 2({\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