A problem of Hooley in Diophantine approximation
Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 299-308

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In [5] Professor Hooley announced without proof the following result which is a variant of well-known work by Heilbronn [4]and Danicic [3] (see [1]).Let k≥2 be an integer, b a fixed non-zero integer, and a an irrational real number. Then, for any ɛ> 0, there are infinitely many solutions to the inequalityHere
Harman, Glyn. A problem of Hooley in Diophantine approximation. Glasgow mathematical journal, Tome 38 (1996) no. 3, pp. 299-308. doi: 10.1017/S0017089500031724
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[1] 1.Baker, R. C., Diophantine inequalities, London Math. Soc. Monographs N.S.I (Oxford Science Publications, 1986). Google Scholar

[2] 2.Baker, R. C. and Harman, G., On the distribution of apk modulo one, Mathematika 38 (1991), 170–184. Google Scholar | DOI

[3] 3.Dancic, I., An extension of a theorem of Heilbronn, Mathematika 5 (1958), 30–37. Google Scholar | DOI

[4] 4.Heilbronn, H. A., On the distribution of the sequence θn 2 (mod 1), Quart. J. Math. Oxford Ser. 2, 19 (1948), 249–256. Google Scholar | DOI

[5] 5.Hooley, C., On the location of the roots of polynomial congruences, Glasgow Math. J. 32 (1990), 309–316. Google Scholar | DOI

[6] 6.Hooley, C., On an elementary inequality in the theory of Diophantine approximation, in Analytic Number Theory, Proceedings of a conference in honour of Heini Hallerstam (Birkhauser, 1996), 471–486. Google Scholar

[7] 7.Wooley, T. D., The application of a new mean value theorem to the fractional parts of polynomials, Ada Arith. 65(1993), 163–179. Google Scholar | DOI

[8] 8.Zaharescu, A., Small values of an 2 (mod 1), Invent. Math. 121 (1995), 379–388. Google Scholar | DOI

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