An explicit version of Birch's Theorem

• Autorzy: Trevor D. Wooley
• Języki publikacji: EN

Kategorie tematyczne

• 11G35: Varieties over global fields
• 11E76: Forms of degree higher than two
• 14G05: Rational points
• 11D72: Equations in many variables

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 1
• Strony: 79-96

Daty

wydano

1998

otrzymano

1997-09-26

Twórcy

autor

Trevor D. Wooley

• Department of Mathematics, University of Michigan, East Hall, 525 East University Avenue, Ann Arbor, Michigan 48109-1109, U.S.A.

Bibliografia

• [1] B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102-105.
• [2] B. J. Birch, Forms in many variables, Proc. Roy. Soc. London Ser. A 265 (1961/62), 245-263.
• [3] J. Brüdern and R. J. Cook, On simultaneous diagonal equations and inequalities, Acta Arith. 62 (1992), 125-149.
• [4] H. Davenport, Cubic forms in thirty-two variables, Philos. Trans. Roy. Soc. London Ser. A 251 (1959), 193-232.
• [5] H. Davenport, Cubic forms in 16 variables, Proc. Roy. Soc. London Ser. A 272 (1963), 285-303.
• [6] H. Davenport and D. J. Lewis, Simultaneous equations of additive type, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 557-595.
• [7] D. B. Leep and W. M. Schmidt, Systems of homogeneous equations, Invent. Math. 71 (1983), 539-549.
• [8] D. J. Lewis and R. Schulze-Pillot, Linear spaces on the intersection of cubic hypersurfaces, Monatsh. Math. 97 (1984), 277-285.
• [9] L. Low, J. Pitman and A. Wolff, Simultaneous diagonal congruences, J. Number Theory 36 (1990), 1-11.
• [10] W. M. Schmidt, On cubic polynomials IV. Systems of rational equations, Monatsh. Math. 93 (1982), 329-348.
• [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.
• [12] W. M. Schmidt, The density of integer points on homogeneous varieties, Acta Math. 154 (1985), 243-296.
• [13] V. A. Tartakovskiĭ, Die asymptotische Gesetze der 'allgemeinen' Diophantischen Analyse mit vielen Unbekannten, Izv. Akad. Nauk SSSR Ser. Mat.-Fiz. 1935, 483-524.
• [14] T. D. Wooley, On the local solubility of diophantine systems, Compositio Math. 111 (1998), 149-165.
• [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.