Lattice points in bodies of revolution

• Autorzy: Fernando Chamizo
• Języki publikacji: EN

Kategorie tematyczne

• 11P21: Lattice points in specified regions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 85
• Numer: 3
• Strony: 265-277

Daty

wydano

1998

otrzymano

1997-07-27

poprawiono

1998-01-30

Twórcy

autor

Fernando Chamizo

• Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049-Madrid, Spain

Bibliografia

• [Ch-Iw] F. Chamizo and H. Iwaniec, On the sphere problem, Rev. Mat. Iberoamericana 11 (1995), 417-429.
• [Ch] J.-R. Chen, Improvement on the asymptotic formulas for the number of lattice points in a region of the three dimensions (II), Sci. Sinica 12 (1963), 751-764.
• [Ga] C. F. Gauss, De nexu inter multitudinem classium, in quas formae binariae secundi gradus distribuntur, earumque determinantem [II] (1837); Werke, Band 2, 269-291.
• [Gr-Ko] S. W. Graham and G. Kolesnik, Van der Corput's Method of Exponential Sums, London Math. Soc. Lecture Note Ser. 126, Cambridge Univ. Press, Cambridge, 1991.
• [H-B] D. R. Heath-Brown, Lattice points in the sphere, preprint, 1997. (To appear in the Proceedings of the Number Theory Conference held in Zakopane, Poland, 1997.)
• [He] C. S. Herz, Fourier transforms related to convex sets, Ann. of Math. 75 (1962), 81-92.
• [Hl] E. Hlawka, Über Integrale auf konvexen Körpern I, Monatsh. Math. 54 (1950), 1-36.
• [Hu] M. N. Huxley, Exponential sums and lattice points II, Proc. London Math. Soc. (3) 66 (1993), 279-301.
• [Iv] A. Ivić, The Riemann Zeta-Function, Wiley, 1985.
• [Kr] E. Krätzel, Lattice Points, Kluwer, Dordrecht, 1988.
• E. Krätzel and W. G. Nowak, Lattice points in large convex bodies, II, Acta Arith. 62 (1992), 285-295.
• [Sp] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. II, 2nd ed., Publish or Perish, 1979.
• [Ti] E. C. Titchmarsh, The lattice-points in a circle, Proc. London Math. Soc. (2) 38 (1934), 96-115.
• [Vi] I. M. Vinogradov, On the number of integer points in a sphere, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1963), 957-968 (in Russian).