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We show how the Selberg $\Lambda^2$-sieve can be used to obtain power saving error terms in a wide class of counting problems which are tackled using geometry of numbers.
H.Iwaniec and E.Kowalski, Analytic Number Theory, Amer. Math. Soc. Colloq. Publ
2004
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M. Bhargava, Higher composition laws IV. The parametrization of quintic rings. Ann. of Math. ( ( 2 ) )
2008
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J. Brakenhoff, Counting problem for number rings, Ph.D thesis, Lieden University, 2009
2009
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2009
Cited alongside, same era.
K. Belabas, M. Bhargava, and C. Pomerance, Error terms for the Davenport-Heilbronn theorems, Duke Math. J
2010
Cited alongside, same era.
M. Bhargava, The density of discriminants of quartic rings and fields, Ann. of Math
Cited in the paper.
M. Bhargava, Most hyperelliptic curves over Q have no rational points, arxiv/1308.0395
Cited in the paper.
M. Bhargava and A. Shankar, Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves, preprint
Cited in the paper.
M. Bhargava and A. Shankar, The average number of elements in the 5 5 -Selmer group of elliptic curves, in preparation
Cited in the paper.
A. Shankar and X. Wang, The average size of the 2 2 -Selmer group for monic even hyperelliptic curves, arXiv/1307.3531
Cited in the paper.
M. Bhargava, The density of discriminants of quintic rings and fields, Ann. of Math. ( ( 2 ) )
2010
Later among the works it cites.
M. Bhargava and B. Gross, The average size of the 2-Selmer gro up of Jacobians of hyperelliptic curves having a rational Weierstrass point (2012), arXiv/1208.1007
2012
Later among the works it cites.
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