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We develop a method for determining the density of squarefree values taken by certain multivariate integer polynomials that are invariants for the action of an algebraic group on a vector space.
F. Levi, Kubische Zahlkörper und binäre kubische Formenklassen, Leipz. Ber
1914
Earlier work this paper cites.
H. Davenport, On the class-number of binary cubic forms I and II, J. London Math. Soc
1951
Earlier work this paper cites.
B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree
1964
Earlier work this paper cites.
C. Hooley, On the power free values of polynomials, Mathematika
1967
Earlier work this paper cites.
K. Uchida, Unramified extensions of quadratic number fields II, Tôhoku Math. J
1970
Earlier work this paper cites.
Y. Yamamoto, On unramified Galois extensions of quadratic number fields, Osaka J. Math
1970
Earlier work this paper cites.
H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields II, Proc. Roy. Soc. London Ser. A
1971
Earlier work this paper cites.
M. Sato and T. Kimura, A classification of irreducible prehomogeneous vector spaces and their relative invariants, Nagoya Math. J
1977
Earlier work this paper cites.
H. Cohen and H. W. Lenstra, Heuristics on class groups of number fields, Number theory, Noordwijkerhout, 1983
1984
Earlier work this paper cites.
K. Yamamura, On unramified Galois extensions of real quadratic number fields, Osaka J. Math
1986
Earlier work this paper cites.
B. Datskovsky and D. J. Wright, Density of discriminants of cubic extensions, J. Reine Angew. Math
1988
Earlier work this paper cites.
T. Ekedahl, An infinite version of the Chinese remainder theorem, Comment. Math. Univ. St. Paul
1991
Earlier work this paper cites.
G. Greaves, Power-free values of binary forms, Quart. J. Math. Oxford Ser. (2)
1992
Cited alongside, same era.
D. J. Wright and A. Yukie, Prehomogeneous vector spaces and field extensions, Invent. Math
1992
Cited alongside, same era.
T. Kondo, Algebraic number fields with the discriminant equal to that of a quadratic number field, J. Math. Soc. Japan
1995
Cited alongside, same era.
J. Nakagawa, Orders of a quartic field, Mem. Amer. Math. Soc
1996
Cited alongside, same era.
A. Granville, ABC allows us to count squarefrees, Internat. Math. Res. Notices
1998
Cited alongside, same era.
B. Poonen, Bertini theorems over finite fields, Ann. of Math
2004
Later among the works it cites.
M. Bhargava, The density of discriminants of quartic rings and fields, Ann. of Math
2005
Later among the works it cites.
M. Bhargava, Mass formulae for extensions of local fields, and conjectures on the density of number field discriminants, Int. Math. Res. Not
2007
Later among the works it cites.
M. Bhargava, Higher composition laws IV: The parametrization of quintic rings, Ann. of Math
2008
Later among the works it cites.
T. Fisher, The invariants of a genus one curve, Proc. Lond. Math. Soc. (3)
2008
Later among the works it cites.
J. Brakenhoff, Counting problems for number rings
2009
Later among the works it cites.
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1998
Cited alongside, same era.
B. Poonen and M. Stoll, The Cassels–Tate pairing on polarized abelian varieties, Ann. of Math
1999
Cited alongside, same era.
W.-T. Gan, B. H. Gross, and G. Savin, Fourier coefficients of modular forms on G 2 G_{2} , Duke Math. J
2002
Cited alongside, same era.
D. R. Heath-Brown, The density of rational points on curves and surfaces, Ann. of Math. (2)
2002
Cited alongside, same era.
B. Poonen, Squarefree values of multivariable polynomials, Duke Math. J
2003
Cited alongside, same era.
M. Bhargava, Higher composition laws III: The parametrization of quartic rings, Ann. of Math
2004
Cited alongside, same era.
M. Bhargava and B. Gross, Arithmetic invariant theory, http://arxiv.org/abs/1208.1007
Cited in the paper.
K. Belabas, M. Bhargava, and C. Pomerance, Error terms for the Davenport–Heilbronn theorems, Duke Math. J
2010
Later among the works it cites.
M. Bhargava, The density of discriminants of quintic rings and fields, Ann. of Math
2010
Later among the works it cites.
P. Salberger and T. Wooley, Rational points on complete intersections of higher degree, and mean values of Weyl sums, J. Lond. Math. Soc. (2)
2010
Later among the works it cites.
K. S. Kedlaya, A construction of polynomials with squarefree discriminants, Proc. Amer. Math. Soc
2012
Later among the works it cites.
M. M. Wood, Quartic rings associated to binary quartic forms, Int. Math. Res. Not
2012
Later among the works it cites.