Amod's Mathematics Research

Some Information

• CV:    dvi, ps, pdf.
  

Papers/preprints

• The torsion and component groups and the Birch and Swinnerton-Dyer conjecture, in progress.
  
• A visible factor of the special L-value (with L. Merel), preprint:    ps, pdf.
  
• The Manin constant, congruence primes and the modular degree (with K. Ribet and W. Stein), preprint: 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.~1--17. ps, pdf.
  
• Visible evidence for the Birch and Swinnerton-Dyer 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, 455--484. ps, pdf.
  
• Visibility of Shafarevich-Tate Groups of Abelian Varieties (with W.Stein), J. Number Theory 97 (2002), no. 1, 171--185.    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, 303--311. ps, pdf.
  An earlier non-appendix version: ps, pdf.
  
• On invisible elements of the Tate-Shafarevich group, C. R. Acad. Sci. Paris Ser. I Math. 328 (1999), no. 5, 369--374. 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 Shimura 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 my paper with William Stein on the Manin constant above for the correct statements). dvi    

Slides from some talks

• 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.