An explicit version of Birch's Theorem

Trevor D. Wooley

Acta Arithmetica (1998)

  • Volume: 85, Issue: 1, page 79-96
  • ISSN: 0065-1036

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Trevor D. Wooley. "An explicit version of Birch's Theorem." Acta Arithmetica 85.1 (1998): 79-96. <http://eudml.org/doc/207155>.

@article{TrevorD1998,
author = {Trevor D. Wooley},
journal = {Acta Arithmetica},
keywords = {homogeneous polynomials; rational zero; zeros of forms; Birch's theorem},
language = {eng},
number = {1},
pages = {79-96},
title = {An explicit version of Birch's Theorem},
url = {http://eudml.org/doc/207155},
volume = {85},
year = {1998},
}

TY - JOUR
AU - Trevor D. Wooley
TI - An explicit version of Birch's Theorem
JO - Acta Arithmetica
PY - 1998
VL - 85
IS - 1
SP - 79
EP - 96
LA - eng
KW - homogeneous polynomials; rational zero; zeros of forms; Birch's theorem
UR - http://eudml.org/doc/207155
ER -

References

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  1. [1] B. J. Birch, Homogeneous forms of odd degree in a large number of variables, Mathematika 4 (1957), 102-105. Zbl0081.04501
  2. [2] B. J. Birch, Forms in many variables, Proc. Roy. Soc. London Ser. A 265 (1961/62), 245-263. Zbl0103.03102
  3. [3] J. Brüdern and R. J. Cook, On simultaneous diagonal equations and inequalities, Acta Arith. 62 (1992), 125-149. Zbl0774.11015
  4. [4] H. Davenport, Cubic forms in thirty-two variables, Philos. Trans. Roy. Soc. London Ser. A 251 (1959), 193-232. Zbl0084.27202
  5. [5] H. Davenport, Cubic forms in 16 variables, Proc. Roy. Soc. London Ser. A 272 (1963), 285-303. Zbl0107.04102
  6. [6] H. Davenport and D. J. Lewis, Simultaneous equations of additive type, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 557-595. Zbl0207.35304
  7. [7] D. B. Leep and W. M. Schmidt, Systems of homogeneous equations, Invent. Math. 71 (1983), 539-549. Zbl0504.10010
  8. [8] D. J. Lewis and R. Schulze-Pillot, Linear spaces on the intersection of cubic hypersurfaces, Monatsh. Math. 97 (1984), 277-285. Zbl0546.10018
  9. [9] L. Low, J. Pitman and A. Wolff, Simultaneous diagonal congruences, J. Number Theory 36 (1990), 1-11. Zbl0643.10011
  10. [10] W. M. Schmidt, On cubic polynomials IV. Systems of rational equations, Monatsh. Math. 93 (1982), 329-348. Zbl0481.10015
  11. [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. [12] W. M. Schmidt, The density of integer points on homogeneous varieties, Acta Math. 154 (1985), 243-296. Zbl0561.10010
  13. [13] V. A. Tartakovskiĭ, Die asymptotische Gesetze der 'allgemeinen' Diophantischen Analyse mit vielen Unbekannten, Izv. Akad. Nauk SSSR Ser. Mat.-Fiz. 1935, 483-524. Zbl61.1068.01
  14. [14] T. D. Wooley, On the local solubility of diophantine systems, Compositio Math. 111 (1998), 149-165. Zbl0892.11011
  15. [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. Zbl0905.11022

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