Pairs of additive quadratic forms modulo one
R. C. Baker ; S. Schäffer
Acta Arithmetica, Tome 62 (1992), p. 45-59 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1992-01-01
EUDML-ID : urn:eudml:doc:206479 
@article{bwmeta1.element.bwnjournal-article-aav62i1p45bwm,
     author = {R. C. Baker and S. Sch\"affer},
     title = {Pairs of additive quadratic forms modulo one},
     journal = {Acta Arithmetica},
     volume = {62},
     year = {1992},
     pages = {45-59},
     zbl = {0729.11032},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav62i1p45bwm}
}

R. C. Baker; S. Schäffer. Pairs of additive quadratic forms modulo one. Acta Arithmetica, Tome 62 (1992) pp. 45-59. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav62i1p45bwm/

[000] [1] R. C. Baker, Small solutions of congruences, Mathematika 20 (1983), 164-188. | Zbl 0532.10011

[001] [2] R. C. Baker, Diophantine Inequalities, Oxford University Press, Oxford 1986. | Zbl 0592.10029

[002] [3] R. C. Baker and J. Brüdern, Pairs of quadratic forms modulo one, Glasgow Math. J., to appear. | Zbl 0774.11031

[003] [4] R. C. Baker and J. Gajraj, On the fractional parts of certain additive forms, Math. Proc. Cambridge Philos. Soc. 79 (1976), 463-467. | Zbl 0323.10032

[004] [5] R. C. Baker and G. Harman, Small fractional parts of quadratic and additive forms, Math. Proc. Cambridge Philos. Soc. 90 (1981), 5-12. | Zbl 0466.10029

[005] [6] R. C. Baker and G. Harman, Small fractional parts of quadratic forms, Proc. Edinburgh Math. Soc. 25 (1982), 269-277. | Zbl 0499.10037

[006] [7] R. J. Cook, The fractional parts of an additive form, Proc. Cambridge Philos. Soc. 72 (1972), 209-212. | Zbl 0237.10023

[007] [8] I. Danicic, Contributions to number theory, Ph. D. thesis, London 1957.

[008] [9] I. Danicic, An extension of a theorem of Heilbronn, Mathematika 5 (1958), 30-37. | Zbl 0085.03304

[009] [10] I. Danicic, On the fractional parts of θx² and ϕx², J. London Math. Soc. 34 (1959), 353-357. | Zbl 0088.25704

[010] [11] I. Danicic, The distribution (mod 1) of pairs of quadratic forms with integer variables, J. London Math. Soc. 42 (1967), 618-623. | Zbl 0165.36402

[011] [12] G. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge University Press, Cambridge 1967.

[012] [13] G. Harman, Diophantine approximation and prime numbers, Ph.D. thesis, London 1982. | Zbl 0443.10015

[013] [14] D. R. Heath-Brown, Small solutions of quadratic congruences II, Mathematika 38 (1991), 264-284. | Zbl 0725.11018

[014] [15] H. Heilbronn, On the distribution of the sequence θn² (mod 1), Quart. J. Math. Oxford Ser. (2) 19 (1948), 249-256. | Zbl 0031.20502

[015] [16] M. C. Liu, On the fractional parts of θnk and ϕnk, Quart. J. Math. Oxford Ser. (2) 21 (1970), 481-486.

[016] [17] M. C. Liu, Simultaneous approximation of two additive forms, Trans. Amer. Math. Soc. 206 (1975), 361-373. | Zbl 0305.10024

[017] [18] A. Schinzel, H. P. Schlickewei and W. M. Schmidt, Small solutions of quadratic congruences and small fractional parts of quadratic forms, Acta Arith. 37 (1980), 241-248. | Zbl 0446.10026

[018] [19] W. M. Schmidt, Small fractional parts of polynomials, CBMS Regional Conf. Ser. in Math. 32, Amer.Math. Soc., Providence 1977.