Manjul Bhargava - Selected Publications

Selected Publications

• Bhargava, Manjul (2000). "The Factorial Function and Generalizations". The American Mathematical Monthly 107 (9): 783–799. doi:10.2307/2695734. http://mathdl.maa.org/images/upload_library/22/Hasse/00029890.di021346.02p0064l.pdf.
• Bhargava, Manjul (2004). "Higher Composition Laws I: A New View on Gauss Composition, and Quadratic Generalizations". The Annals of Mathematics 159: 217–250. doi:10.4007/annals.2004.159.217. http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n1-p03.pdf.
• Bhargava, Manjul (2004). "Higher Composition Laws II: On Cubic Analogues of Gauss Composition". The Annals of Mathematics 159 (2): 865–886. doi:10.4007/annals.2004.159.865. http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n2-p09.pdf.
• Bhargava, Manjul (2004). "Higher Composition Laws III: The Parametrization of Quartic Rings". The Annals of Mathematics 159 (3): 1329–1360. doi:10.4007/annals.2004.159.1329. http://annals.math.princeton.edu/wp-content/uploads/annals-v159-n3-p08.pdf.
• Bhargava, Manjul (2005). "The density of discriminants of quartic rings and fields". The Annals of Mathematics 162: 1031–1063. doi:10.4007/annals.2005.162.1031. http://annals.math.princeton.edu/wp-content/uploads/annals-v162-n2-p10.pdf.
• Bhargava, Manjul (2008). "Higher composition laws IV: The parametrization of quintic rings". The Annals of Mathematics 167: 53–94. doi:10.4007/annals.2008.167.53. http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n1-p02.pdf.
• Bhargava, Manjul (2010). "The density of discriminants of quintic rings and fields". The Annals of Mathematics 172: 1559–1591. doi:10.4007/annals.2010.172.1559. http://annals.math.princeton.edu/wp-content/uploads/annals-v162-n2-p10.pdf.
• Bhargava, Manjul; Shankar, Arul (2010). Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves.
• Bhargava, Manjul; Shankar, Arul (2010). Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0. arXiv:1007.0052.
• Bhargava, Manjul; Satriano, Matthew (2010). On a notion of "Galois closure" for extensions of rings. arXiv:1006.2562v1.