An explicit version of Birch's Theorem
Trevor D. Wooley
Acta Arithmetica, Tome 84 (1998), p. 79-96 / Harvested from The Polish Digital Mathematics Library
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     title = {An explicit version of Birch's Theorem},
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     volume = {84},
     year = {1998},
     pages = {79-96},
     zbl = {0915.11021},
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Trevor D. Wooley. An explicit version of Birch's Theorem. Acta Arithmetica, Tome 84 (1998) pp. 79-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav85i1p79bwm/

[000] [1] B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102-105. | Zbl 0081.04501

[001] [2] B. J. Birch, Forms in many variables, Proc. Roy. Soc. London Ser. A 265 (1961/62), 245-263. | Zbl 0103.03102

[002] [3] J. Brüdern and R. J. Cook, On simultaneous diagonal equations and inequalities, Acta Arith. 62 (1992), 125-149. | Zbl 0774.11015

[003] [4] H. Davenport, Cubic forms in thirty-two variables, Philos. Trans. Roy. Soc. London Ser. A 251 (1959), 193-232. | Zbl 0084.27202

[004] [5] H. Davenport, Cubic forms in 16 variables, Proc. Roy. Soc. London Ser. A 272 (1963), 285-303. | Zbl 0107.04102

[005] [6] H. Davenport and D. J. Lewis, Simultaneous equations of additive type, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 557-595. | Zbl 0207.35304

[006] [7] D. B. Leep and W. M. Schmidt, Systems of homogeneous equations, Invent. Math. 71 (1983), 539-549. | Zbl 0504.10010

[007] [8] D. J. Lewis and R. Schulze-Pillot, Linear spaces on the intersection of cubic hypersurfaces, Monatsh. Math. 97 (1984), 277-285. | Zbl 0546.10018

[008] [9] L. Low, J. Pitman and A. Wolff, Simultaneous diagonal congruences, J. Number Theory 36 (1990), 1-11. | Zbl 0643.10011

[009] [10] W. M. Schmidt, On cubic polynomials IV. Systems of rational equations, Monatsh. Math. 93 (1982), 329-348. | Zbl 0481.10015

[010] [11] W. M. Schmidt, Analytic methods for congruences, Diophantine equations and approximations, in: Proceedings of the International Congress of Mathematicians (Warsaw, 1983), Vol. 1, PWN, Warszawa, 1984, 515-524.

[011] [12] W. M. Schmidt, The density of integer points on homogeneous varieties, Acta Math. 154 (1985), 243-296. | Zbl 0561.10010

[012] [13] V. A. Tartakovskiĭ, Die asymptotische Gesetze der 'allgemeinen' Diophantischen Analyse mit vielen Unbekannten, Izv. Akad. Nauk SSSR Ser. Mat.-Fiz. 1935, 483-524. | Zbl 61.1068.01

[013] [14] T. D. Wooley, On the local solubility of diophantine systems, Compositio Math. 111 (1998), 149-165. | Zbl 0892.11011

[014] [15] T. D. Wooley, Forms in many variables, in: Analytic Number Theory: Proceedings of the 39th Taniguchi International Symposium, Kyoto, May 1996, Y. Motohashi (ed.), London Math. Soc. Lecture Note Ser. 247, Cambridge Univ. Press, 1997, 361-376. | Zbl 0905.11022