Siberian Mathematical Journal

, Volume 31, Issue 5, pp 833–839 | Cite as

On the Rankin-Sobolev problem regarding extrema of Epstein's zeta-function. Estimate of the origin of the ray of extremality of Voronoi's second perfect form

  • S. Sh. Shushbaev
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Perfect Form 

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Literature Cited

  1. 1.
    R. A. Rankin, “A minimum problem for the Epstein zeta-function,” Proc. Glasgow Math. Assoc.,1, 149–168 (1953).Google Scholar
  2. 2.
    S. L. Sobolev, Introduction to the Theory of Cubature Formulas [in Russian], Nauka, Moscow (1975).Google Scholar
  3. 3.
    B. N. Delone and S. S. Ryshkov, “On the theory of the extrema of a mltidimensional ζ-function,” Dokl. Akad. Nauk SSSR,173, No. 4, 991–994 (1967).Google Scholar
  4. 4.
    S. S. Ryshkov, “On the question of the final ξ-optimality of lattices that yield the densest packing of n-dimensional balls,” Sib. Mat. Zh.,14, No. 6, 1065–1075 (1973).Google Scholar
  5. 5.
    S. Sh. Shushbaev, “On the Rankin-Sobolev problem on extrema of Epstein's zeta-function. On the origin of the extremality ray of the principal perfect form,” Izv. Akad. Nauk UzSSR, Ser. Fiz.-Mat. Nauk No. 1, 33–39 (1978).Google Scholar
  6. 6.
    S. Sh. Shushbaev, “On the Rankin-Sobolev problem of the multidimensional zeta-function (estimate of the origin of the ray of extremality of the principal perfect form),” Trudy Mat. Inst. Akad. Nauk SSSR,152, 232–235 (1980).Google Scholar
  7. 7.
    G. Voronoi, “Sur quelques propriétés des formes quadratiques positives perfaites,” J. Reine Angew. Math.,133, 97–178 (1908); Collected Works, Vol. 2, Izd. Akad. Nauk UkrSSR, Kiev (1952), pp. 171–214.Google Scholar
  8. 8.
    K. M. Éndibaev, “On an extremal problem for the four-dimensional Epstein ζ-function,” Dokl. Akad. Nauk UzSSR, No. 4, 18–21 (1978).Google Scholar
  9. 9.
    S. S. Ryshkov and S. Sh. Shushbaev “Positive forms of degree 2l>2 and zeta-separating quadratic forms,” Dokl. Akad. Nauk SSSR,269, No. 6, 1316–1319 (1983).Google Scholar
  10. 10.
    K. M. Éndibaev and S. Sh. Shushbaev, A refined estimate of the origin of the ray of extremality of the form corresponding to the densest packing of five-dimensional balls. Manuscript deposited at VINITI, May 11, 1982, No. 2376-82.Google Scholar
  11. 11.
    S. S. Ryshkov and E. P. Baranovskii, “Classical methods of the theory of lattice packings,” Uspekhi Mat. Nauk,34, No. 4, 3–63 (1979).Google Scholar
  12. 12.
    E. P. Baranovskii, S. S. Ryshkov, and S. Sh. Shushbaev, “A geometric estimate of the number of representations of a real number by a positive quadratic form and an estimate of the remainder term of the multidimensional zeta function,” Trudy Mat. Inst. Akad. Nauk SSSR,158, 3–8 (1981).Google Scholar

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© Plenum Publishing Corporation 1991

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  • S. Sh. Shushbaev

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