Anupam Srivastav
Email : asrivastav@math.albany.edu
Fax (department) : (518) 4424731
Ph.D.
University of Illinois at UrbanaChampaign (Advisors : I. Reiner,
S. V. Ullom).
Research Interests
My area of reseach is in algebraic number theory. I am particularly interested in Galois module theory. There is a nice introduction to some problems in Galois module theory at L. N. Childs' home page. My interest is motivated by relationships between algebroarithmetic invariants and analytic invariants associated with Galois
extension of number fields. If M/K is a Galois extension of number fields with
Galois group G, an algebroarithmetic invariant is associated to the Hmodule S in a classgroup of H, where S is the ring of integers of M and H is the associated order of S in the group algebra KG. Analytic invariants arise from Lfunctions (or padic Lfunctions) associated with number fields K and M.
Much of my work has been about such algebroarithmetic invariants that come from a subgroup of the classgroup of H, called the Swan subgroup. I am also interested in the theory of cyclotomic fields and the arithmetic of elliptic curves.
Invited Lectures

Millennial Conference on Number Theory , University of Illinois at UrbanaChampaign, May 2000.

International Conference on Discrete Mathematics and Number Theory , Tiruchirapalli, India, January 1996.

Workshop on Galois Module Structures, The Fields Institute, Canada, February 1994.
Publications

"Swan modules and elliptic functions", Illinois J. Math. , vol. 32 (3),
1988, 462483.

" A note on Swan modules", Indian J. Pure Appl. Math. , vol. 20 (11), 1989, 10671076.

"Elliptic Curves with Complex Multiplication and Galois module structure"
(with M.J. Taylor ), Invent, Math. , vol. 99, 1990, 165184.

"Modules de Swan et courbes elliptiques a multiplication complexe",
Seminaire de la Theorie des Nombres, Bordeaux, vol. 2, 1990, 4148.

"On Taylor's conjecture for Kummer Orders" (with Ph. CassouNogues ), Seminaire de la Theorie des Nombres, Bordeaux, vol. 2, 1990, 349363.

"On Fueter model and monogenity of ring of integers" (with S. Venkataraman), J. Number Theory, vol. 43 (1), 1993, 4350.

"Relative Galois module structure of quadratic exrensions" (with S. Venkataraman), Indian J. Pure Appl. Math., vol 25 (5), 1994, 473488.

"Unramified quadratic extensions of real quadratic fields, normal integral bases and 2adic Lfunctions" (with S. Venkataraman), J. Number Theory, vol. 67 (2), 1997, 139145.

"Swan Modules and HilbertSpeiser number fields" (with C. Greither , D. R. Replogle and K. Rubin ),
J. Number Theory, vol. 79 (1), 1999, 164173.

"Normal Integral Bases, Swan Modules and pAdic LFunctions", Number Theory for the Millennium III (Urbana, IL, 2000)
, A K Peters, Natick, MA, 2002, 231241.
Doctoral Students ( with current affiliation)
S. Venkataraman, Ph. D., 1992; " On rings of integers of relative abelian extensions of number fields".
Dr. Venkataraman is an Assistant Professor at the IGO University in New Delhi, India.
D. R. Replogle, Ph. D., 1997; "Swan classes and realisable classes for integral group rings over groups of prime order".