Some problems of Diophantine approximation in the theory of the Riemann zeta function

Akio Fujii

Type: Article

Publication Date: 1992-01-01

Citations: 7

DOI: https://doi.org/10.3792/pjaa.68.131

Abstract

Introduction.Let a be a positive number.The distribution of the ractional part {an} of an has been studied extensively.It is well-known that it depends heavily on the arithmetic nature of a.We may briefly recall this act for a quadratic irrational a as follows.It was shown by Hardy-Littlewood [6] and Ostrowski [8] that nx <<logX.Hecke [7] has shown, in act, that if a is JD or 1/JD with a positive square free integer D2 or 3 (mod 4), then for any e0 {n}-lo =A lo X+A lo X+A lo X + CX(/(,o+O(X-,),

Locations

Proceedings of the Japan Academy Series A Mathematical Sciences - View - PDF

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+	On the distribution of imaginary parts of zeros of the Riemann zeta function, II	2008	Kevin Ford K. Soundararajan Alexandru Zaharescu
+	Explicit Formulas and Oscillations	1999	Akio Fujii
+	Uniform Distribution of Zeros of Dirichlet Series	2007	Amir Akbary M. Ram Murty
+ PDF Chat	On the distribution of imaginary parts of zeros of the Riemann zeta function	2005	Kevin Ford Alexandru Zaharescu
+	Natural boundaries of a family of Dirichlet series	2013	Alexandru Zaharescu Mohammad Zaki
+ PDF Chat	Some problems of diophantine approximation in the theory of the Riemann zeta function, II	1993	Akio Fujii
+ PDF Chat	Relation between primes and nontrivial zeros in the Riemann hypothesis; Legendre polynomials, modified zeta function and Schrödinger equation	2012	Seong-Soo Choi J. W. Chung Kwang S. Kim

Works Cited by This (6)

Action	Title	Year	Authors
+ PDF Chat	On a theorem of Landau, II	1990	Akio Fujii
+ PDF Chat	Some problems of Diophantine approximation: The lattice-points of a right-angled triangle. (Second memoir.)	1922	G. H. Hardy J. E. Littlewood
+	On the distribution of <i>αp</i> modulo 1	1977	R. C. Vaughan
+	Diophantine approximation, Kronecker's limit formula and the Riemann Hypothesis	1989	Akio Fujii
+	On the Zeros of Dirichlet L-Functions. III	1976	Akio Fujii
+	Diophantine Approximation and its Applications	2009	R. Tijdeman