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| * H.P.F. Swinnerton-Dyer. The effect of twisting on the 2-Selmer group. Math. Proc. Cambridge Philos. Soc. 145 (2008) 513-526. * prereq(?): Heath-Brown paper * Dan Kane... (?) |
* Reading list: * MR1292115 (95h:11064) Heath-Brown, D. R. The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Invent. Math. 118 (1994), no. 2, 331–370. * MR2464773 (2010d:11059) Swinnerton-Dyer, Peter. The effect of twisting on the 2-Selmer group. Math. Proc. Cambridge Philos. Soc. 145 (2008), no. 3, 513–526. * Kane, Daniel. On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve. Preprint. http://arxiv.org/pdf/1009.1365v1 |
Temporary wiki for organizing the informal reading groups at the Arithmetic Statistics program at MSRI.
This is an example of how to make a separate subpage correctly.
Cohen-Lenstra heuristics
- chair: Bjorn Poonen
- The first meeting of the reading group will be Tuesday, January 18, 11-12. It will be in the 2nd floor seminar room if that room is available.
- Informal reading group on the Cohen-Lenstra heuristics
- Reading list (in increasing order of sophistication):
- MR0750661 Cohen, H. ; Lenstra, H. W., Jr. Heuristics on class groups. Number theory (New York, 1982), 26--36, Lecture Notes in Math., 1052, Springer, Berlin, 1984.
- MR0756082 (85j:11144) Cohen, H. ; Lenstra, H. W., Jr. Heuristics on class groups of number fields. Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983), 33--62, Lecture Notes in Math., 1068, Springer, Berlin, 1984.
- MR1837670 (2003a:11065) Delaunay, Christophe. Heuristics on Tate-Shafarevitch groups of elliptic curves defined over Q. Experiment. Math. 10 (2001), no. 2, 191--196.
PDFs of these three papers have been placed in my public directory at MSRI, which I think can be accessed by typing cd ~bpoonen/Public at a terminal prompt.
Iwaniec-Luo-Sarnak
- chair: Kaneenika Sinha
- times: Wednesdays 11-12
- H. Iwaniec, W. Luo, and, P. Sarnak, Low lying zeros of families of L-functions, Publ. IHES, 2000.
there is also a study guide and reading list by Steven Miller, at Williams: http://www.williams.edu/go/math/sjmiller/public_html/ntandrmt/
Bhargava-Shankar
- chair: Barry Mazur
- times: Thursdays 11-12
- pp. 2-9 (i.e., the Introduction) of Binary quadratic forms having bounded invariants, and the boundedness of average ranks of elliptic curves
Quadratic twists of elliptic curves: 2-Selmer ranks
- chair: Jamie Weigandt
- times: Fridays 11-12
- Reading list:
- MR1292115 (95h:11064) Heath-Brown, D. R. The size of Selmer groups for the congruent number problem. II. With an appendix by P. Monsky. Invent. Math. 118 (1994), no. 2, 331–370.
- MR2464773 (2010d:11059) Swinnerton-Dyer, Peter. The effect of twisting on the 2-Selmer group. Math. Proc. Cambridge Philos. Soc. 145 (2008), no. 3, 513–526.
Kane, Daniel. On the Ranks of the 2-Selmer Groups of Twists of a Given Elliptic Curve. Preprint. http://arxiv.org/pdf/1009.1365v1
General question group
- (e.g., average ap ’s, Sato-Tate (the statement), etc.) Not yet scheduled.