Published: 1978 Received: April 26, 1976Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: 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> λjfj(pj), 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 ∑Kj=1λjfj(pj), 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.
Date of correction: October 20, 2006Reason for correction: -Correction: PDF FILEDetails: -