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Bagchi, B. , The statistical behaviour and universality properties of the Riemann zeta-function and other allied Dirichlet series , PhD Thesis, Calcutta, Indian Statistical Institute, 1981

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References [1] Bettin , S. 2010 The second moment of the Riemann zeta-function with unbounded shifts Int. J. Number Theory

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1 Introduction Let s = σ + it be a complex variable, and α , 0 < α ⩽ 1, be a fixed parameter. The Hurwitz zeta-function ζ ( s,α ) was introduced in [ 6 ], and is defined, for σ > 1, by the Dirichlet series ζ ( s , α ) = ∑ m = 0 ∞ 1 ( m + α

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Abstract  

A. Beurling introduced harmonic functions attached to measurable functions satisfying suitable conditions and defined their spectral sets. The concept of spectral sets is closely related to approximations by trigonometric polynomials. In this paper we consider spectral sets of the harmonic functions attached to the Riemann zeta-function and its modification.

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Summary  

A. Beurling introduced the concept of spectral sets of unbounded functions to study the possibility of the approximation of those by trigonometric polynomials. We consider spectral sets of unbounded functions in a certain class which contains the square of the Riemann zeta-function as a typical example.

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