Nagoya Mathematical Journal

On the distribution (mod $1$) of polynomials of a prime variable

Ming Chit Liu and Kai Man Tsang

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 85 (1982), 241-249.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118786664

Mathematical Reviews number (MathSciNet)
MR0648426

Zentralblatt MATH identifier
0445.10027

Subjects
Primary: 10F40

Citation

Liu, Ming Chit; Tsang, Kai Man. On the distribution (mod $1$) of polynomials of a prime variable. Nagoya Math. J. 85 (1982), 241--249. https://projecteuclid.org/euclid.nmj/1118786664


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References

  • [1] H. Davenport and H. Heilbronn, On indefinite quadratic forms in five variables, J. London Math. Soc,21 (1946), 185-193.
  • [2] H. Davenport and K. F. Roth, The solubility of certain diophantine inequalities, Mathematika, 2 (1955), 81-96.
  • [3] H. Davenport, On a theorem of Heilbronn, Quart. J. Math. Oxford, (2), 18 (1967), 339-344.
  • [4] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed. Oxford, 1965.
  • [5] S. Hartman and S. Knapowski, Bemerkungen ber die Bruchteile von pa, Ann. Polon. Math., 3 (1957), 285-287.
  • [6] H. Heilbronn, On the distribution of the sequence nz(mol),Quart. J. Math. Oxford, 19 (1948), 249-256.
  • [7] L. K. Hua, Additive Theory of Prime Numbers, Translations of Mathematical Monographs Vol. 13, Amer. Math. Soc, Providence, R.I. 1965.
  • [8] M. C. Liu, Approximation by a sum of polynomials involving primes, J. Math. Soc. Japan, 30 (1978), 395-412.
  • [9] W. M. Schmidt, Small Fractional Parts of Polynomials, Regional Conference Series in Mathematics No. 32, Amer. Math. Soc. Providence, R.I. 1977.
  • [10] W. M. Schmidt, On the distribution modulo 1 of the sequence an2 n, Canad. J. Math., 29 (1977), 819-826.
  • [11] R. C. Vaughan, On the distribution of ap modulo 1, Mathematika, 24 (1977), 135- 141.
  • [12] I. M. Vinogradov, Analytischer Beweis des Satzes uber die Verteilung der Bruch- teile eines ganzen Polynoms, (in Russian), Bull. Acad. Sci. USSR (6), 21 (1927), 567-578.
  • [13] I. M. Vinogradov, A new estimate of a trigonometric sum containing primes, (in Russian with English summary), Bull. Acad. Sci. USSR ser. Math., 2 (1938), 3-13.
  • [14] I. M. Vinogradov, The Method of Trigonometrical Sums in the Theory of Numbers, New York Interscience 1954. Department of Mathematics University of Hong Kong Hong Kong