Amod's Mathematics Research

Some Information

• CV:    pdf.
  

Papers/preprints

• Squareness in the special L-value, submitted pdf.
  
• A visible factor for analytic rank one, submitted pdf.
  
• Rational torsion in elliptic curves and the cuspidal subgroup, submitted. pdf.
  
• A visible factor of the special L-value, submitted.    pdf.
  
• The modular degree, congruence primes, and multiplicity one (with K. Ribet and W. Stein), submitted: pdf.
  
• The Manin constant (with K. Ribet and W. Stein), Pure and Applied Mathematics Quarterly, 2 (2006), no.~2, 617--636 (Part II of a special issue in honor of John Coates): 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• The Manin constant, congruence primes and the modular degree (with K. Ribet and W. Stein), unpublished older version: ps, pdf.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 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.
  
• 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.
  
• 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 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    

Informal, Expository, etc.:

• The Birch and Swinnerton-Dyer 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 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.