A new form of the circle method, and its application to quadratic forms

Journal fur die Reine und Angewandte Mathematik

Volumn , Issue 481, 1996, Pages 149-206

  Heath Brown, D R ^a  

^a MAGDALEN COLLEGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444451657     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. P. Deligne, La conjecture de Weil. I, Publ. Math. IHES 43 (1973), 273-307.
2. W. Duke, Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math. 92 (1988), 73-90.
3. W. Duke, Lattice points on ellipsoids, Sém. th. nombres Talence 37 (1987-88), 7pp.
4. W. Duke, J. Friedlander and H. Iwaniec, Bounds for automorphic L-function, Invent. Math. 112 (1993), 1-8.
5. D. R. Heath-Brown, Cubic forms in ten variables, Proc. London Math. Soc. (3) 47 (1983), 225-257.
6. C. Hooley, On a new approach to various problems of Waring's type, Recent progr. anal, number th. I, Academic Press, London (1981), 127-191.
7. C. Hooley, Some recent advances in analytical number theory, Proc. Intern. Congr. Math. (1983), 85-97, North-Holland, Amsterdam 1984.
8. C. Hooley, On Waring's problem, Acta Math. 157 (1986), 49-97.
9. C. Hooley, On nonary cubic forms, J. reine angew. Math. 386 (1988), 32-98.
10. H. Iwaniec, Fourier coefficients of modular forms of half-integral weight, Invent. Math. 87 (1987), 385-401.
11. H. Iwaniec, The circle method and the Fourier coefficients of modular forms, Number theory and related topics, Tata Institute of Fundamental Research, Bombay (1989), 47-55.
12. 2, Acta Math. 49 (1926), 407-464.
13. A. V. Malyshev, On the weighted number of integer points on a quadric, Seminars in Mathematics I, Consultants Bureau, New York (1968), 1-30.
14. L. J. Mordell, Diophantine equations, Academic Press, London 1969.
15. B. Z. Moroz, On the representation of large integers by integral ternary positive definite quadratic forms, Astérisque 209 (1992), 275-278.
16. O. T. O'Meara, Introduction to quadratic forms, Springer, Berlin 1963.
17. C. L. Siegel, Equivalence of quadratic forms, Amer. J. Math. 63 (1941), 658-680.
18. B. R. Srinivasan, The lattice point problem of many dimensional hyperboloids III, Math. Ann. 160 (1965), 280-311.
19. E. C. Titchmarsh, The theory of the Riemann Zeta-function, 2nd edition, Oxford University Press, Oxford 1986.
20. R. C. Vaughan, The Hardy-Littlewood method, Cambridge Tracts Math. 80, Cambridge University Press, 1981.
21. G. L. Watson, Integral Quadratic Forms, Cambridge Tracts Math. 51, Cambridge University Press, 1960.