Amod's Mathematics Research
Address: Department of Mathematics, Florida State University,
208 Love Building, Tallahassee, FL 323064510
Phone:
(850) 6448704
Fax:
Email:
agashe@math.fsu.edu
Some Information
Papers/preprints

(with R. Heaton) Computing intersection numbers between abelian varieties
associated to subspaces of modular forms,
J. Symbolic Comput. 57 (2013), 7077
pdf.

(with S. Biswas) Constructing nontrivial elements of the ShafarevichTate group of an abelian variety over a number field. J. Number Theory 133 (2013), no. 6, 1977  1990.

On the notion of visibility of torsors,
Canadian Mathematical Bulletin 56(2013), no. 2, 225228.
pdf.

The special Lvalue of the winding quotient of level a product of two distinct primes, submitted.
pdf.

Conjectures concerning the orders of the torsion subgroup, the
arithmetic component groups, and the cuspidal subgroup, submitted.
pdf.

Appendix on periods, in: V. Pal, Periods of quadratic twists
of elliptic curves, Proc. Amer. Math. Soc. 140 (2012), no. 5, 1513  1525
pdf.

Visibility and the Birch and SwinnertonDyer
conjecture for analytic rank zero, submitted.
pdf.

Modp reducibility, the torsion subgroup, and the ShafarevichTate group,
J. Ramanujan Math. Soc. 26, No. 4 (2011), 357367.
pdf.

The modular number, the congruence number, and multiplicity one, submitted
pdf.

A visible factor of the Heegner index,
Math. Res. Lett. 17 (2010), no. 6, 10651077.
pdf.

Visibility and the Birch and SwinnertonDyer
conjecture for analytic rank one, Int. Math. Res. Not. (IMRN),
Vol. 2009 (2009), No. 15, pp. 28992913
pdf.

Squareness in the special Lvalue and special Lvalues of twists,
Int. J. Number Theory, Vol. 6, No. 5 (2010), 10911111 pdf.

Rational torsion in elliptic curves and the cuspidal subgroup, submitted.
pdf.

The modular degree, congruence primes, and multiplicity one
(with K. Ribet and W. Stein), in
"Number Theory, Analysis and Geometry, In Memory of Serge Lang",
Springer, (2012), 1950,
pdf.

A visible factor of the special Lvalue,
J. Reine Angew. Math. (Crelle's journal), Vol. 644 (2010), 159187.
pdf.

The Manin constant (with K. Ribet and
W. Stein), Pure and Applied Mathematics Quarterly
(special issue in honor of John Coates), 2 (2006), no.~2, 617636 :
pdf.

The Manin constant,
congruence primes, and the modular degree (with K. Ribet and
W. Stein), unpublished older version:
ps,
pdf.

Visible evidence for the Birch and SwinnertonDyer conjecture
for modular abelian varieties of analytic rank zero
(with W. Stein, and with an appendix by J. Cremona and B. Mazur)
Mathematics of Computation
74 (2005), no.~249, 455484.
ps,
pdf.

Constructing elliptic curves with known number of points
over a prime field (with K. Lauter and R. Venkatesan), in
High primes and
misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie
Williams, Fields Institute Communications,
vol.~41, Amer. Math. Soc., Providence, RI,
2004, pp.~117.
ps,
pdf.

Visibility of ShafarevichTate Groups of Abelian
Varieties (with W.Stein),
J. Number Theory 97 (2002), no. 1, 171185.
ps,
pdf.

Appendix on generating the Hecke algebra (with W. Stein), in:
J.C. Lario, R. Schoof,
Some computations with Hecke rings and deformation rings,
Experiment. Math. 11 (2002), no. 2, 303311.
ps,
pdf.
An earlier nonappendix version:
ps,
pdf.

On invisible elements of the TateShafarevich group,
C. R. Acad. Sci. Paris Ser. I Math. 328 (1999), no. 5, 369374.
Abridged version: ps,
pdf.
 Ph.D. Thesis
(Warning: There are some minor mistakes in Chapter 2: some of the results
should be stated only for newform quotients; also the proof of the
result regarding the relation between the Manin constant,
congruence primes and the modular degree has a gap.
Please refer to the Manin constant article
above for the correct statements).
dvi
pdf
Informal, Expository, etc.:

In progress: a book titled "A motivated introduction to
algebraic geometry"
link.

The Birch and SwinnertonDyer conjecture (a proposal for a local grant that is accessible to people in areas related to mathematics)
pdf.

Rational torsion points on elliptic curves (a poster for an informal workshop, again accessible to people in areas related to mathematics)
pdf.
Slides from some talks

AMS national meeting, San Francisco, 2010
pdf. (needs some corrections)

AMS Sectional meeting, Boca Raton
pdf.
(Note: there are some missing figures)

AMS Sectional meeting, Fayetteville
pdf.
(Note: there are some missing figures)

AMS National meeting, San Antonio, and
AMS Sectional meeting, San Francisco
ps,
pdf.
(Note: there is some repetition in the slides,
and some figures are missing)

Barcelona conference on "Modular curves and abelian varieties"
ps,
pdf.

AMS Sectional meeting, Lawrence, Kansas
ps,
pdf.
For some tables, see W. Stein's web pages:
tables1
tables2

AMS National meeting, New Orleans
ps,
pdf.

Millennial conference in Urbana
ps.
pdf.