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Mathematical Notes

, Volume 64, Issue 2, pp 240–250 | Cite as

On the number of summands in the asymptotic formula for the number of solutions to Waring's equation

  • A. V. Ustinov
Article

Abstract

In the paper, an estimate of the number of summands in the asymptotic formula for the number of solutions to Waring's equation is obtained. This is achieved by means of a recurrent process leading to a greater reduction than that in Vinogradov's mean value theorem.

Key words

Waring's problem Waring's equation estimate of the number of summands Fourier coefficients Hardy's equation Vinogradov's mean value theorem 

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References

  1. 1.
    I. M. Vinogradov,The Method of Trigonometric Sums in Number Theory [in Russian], Nauka, Moscow (1980).Google Scholar
  2. 2.
    V. A. Bykovskii, “On systems of inequalities,”Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI),129, 3–33 (1981).MathSciNetGoogle Scholar
  3. 3.
    A. A. Karatsuba, “On systems of congruences,”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR.-Izv.],29, 935–944 (1965).zbMATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1999

Authors and Affiliations

  • A. V. Ustinov
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityUSSR

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