Approximation by a sum of polynomials involving primes

Ming-Chit LIU

doi:10.2969/jmsj/03030395

Ming-Chit LIU

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ジャーナルフリー

1978 年 30 巻 3 号 p. 395-412

DOI https://doi.org/10.2969/jmsj/03030395

詳細

Published: 1978 Received: 1976/04/26 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) A. Baker, On some diophantine inequalities involving primes, J. Reine Angew. Math., 228 (1967), 166-181.
2) H. Davenport, On sums of positive integral kth powers, Amer. J. Math., 64 (1942), 189-198.
3) H. Davenport and H. Heilbronn, On indefinite quadratic forms in five variables, J. London Math. Soc., 21 (1946), 185-193.
4) H. Davenport and K. F. Roth, The solubility of certain diophantine inequalities, Mathematika, 2 (1955), 81-96.
5) L. K. Hua, Additive Theory of Prime Numbers, Translations of Mathematical Monographs Vol. 13, Amer. Math. Soc., Providence, R. I. 1965.
6) L. K. Hua, Su Lung Tao Yeng, Introduction to Number Theory, Science, Peking, 1975.
7) A. E. Ingham, On the estimation of N(σ, T), Quart. J. Math. Oxford, 11(1940), 291-292.
8) M. C. Liu, Diophantine approximation involving primes, J. Reine Angew. Math., 289 (1977), 199-208.
9) K. Ramachandra, On the sums ∑<K><j=1> λ_jf_j(p_j), J. Reine Angew. Math., 262/263(1973), 158-165.
10) W. Schwarz, Über die Lösbarkeit gewisser Ungleichungen durch Primzahlen, J. Reine Angew. Math., 212 (1963), 150-157.
11) R. C. Vaughan, Diophantine approximation by prime numbers, I, Proc. London Math. Soc., (3) 28 (1974), 373-384.
12) R. C. Vaughan, Diophantine approximation by prime numbers, II, Proc. London Math. Soc., (3) 28 (1974), 385-401.
13) I. M. Vinogradov, A new estimation of a trigonometric sum containing primes, (in Russian with English summary), Bull. Acad. Sci. USSR Sér. Math., 2 (1938), 3-13.
14) I. M. Vinogradov, The Method of Trigonometrical Sums in the Theory of Numbers, Interscience, New York, 1954.

Right : [1] A. Baker, On some diophantine inequalities involving primes, J. Reine Angew. Math., 228 (1967), 166-181.
[2] H. Davenport, On sums of positive integral kth powers, Amer. J. Math., 64 (1942), 189-198.
[3] H. Davenport and H. Heilbronn, On indefinite quadratic forms in five variables, J. London Math. Soc., 21 (1946), 185-193.
[4] H. Davenport and K. F. Roth, The solubility of certain diophantine inequalities, Mathematika, 2 (1955), 81-96.
[5] L. K. Hua, Additive Theory of Prime Numbers, Translations of Mathematical Monographs Vol. 13, Amer. Math. Soc., Providence, R. I. 1965.
[6] L. K. Hua, Su Lung Tao Yeng, Introduction to Number Theory, Science, Peking, 1975.
[7] A. E. Ingham, On the estimation of N(σ,T), Quart. J. Math. Oxford, 11 (1940), 291-292.
[8] M. C. Liu, Diophantine approximation involving primes, J. Reine Angew. Math., 289 (1977), 199-208.
[9] K. Ramachandra, On the sums ∑^K_j=1λ_jf_j(p_j), J. Reine Angew. Math., 262/263 (1973), 158-165.
[10] W. Schwarz, Über die Lösbarkeit gewisser Ungleichungen durch Primzahlen, J. Reine Angew. Math., 212 (1963), 150-157.
[11] R. C. Vaughan, Diophantine approximation by prime numbers, I, Proc. London Math. Soc., (3) 28 (1974), 373-384.
[12] R. C. Vaughan, Diophantine approximation by prime numbers, II, Proc. London Math. Soc., (3) 28 (1974), 385-401.
[13] I. M. Vinogradov, A new estimation of a trigonometric sum containing primes, (in Russian with English summary), Bull. Acad. Sci. USSR Sér. Math., 2 (1938), 3-13.
[14] I. M. Vinogradov, The Method of Trigonometrical Sums in the Theory of Numbers, Interscience, New York, 1954.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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