Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \u3c8K(2)(x) :=2 2b0x\u3c8K(1)(t) dt. We prove under GRH (Generalized Riemann Hypothesis) explicit inequalities for the differences |\u3c8K(1) (x)-x2/2| and |\u3c8K(2) (x)-x3/3|. We deduce an efficient algorithm for the computation of the residue of the Dedekind zeta function and a bound on small-norm prime ideals
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Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
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AbstractIn this paper we study generalised prime systems for which the integer counting function NP(...
AbstractIn this work, we study the coefficients of Bazilevic˘ functions and circularly symmetric fun...
AbstractA singular integral equation with a Holderian second member function on [a,b] is considered ...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
AbstractThe precise Sobolev exponent s∞(φn) of the Butterworth refinable function φn associated with...
AbstractIt is known that∑k=0∞(2kk)(2k+1)4k=π2and∑k=0∞(2kk)(2k+1)16k=π3. In this paper we obtain thei...
AbstractThe pointwise approximation properties of the MKZ–Bézier operators Mn,α(f,x) for α≥1 have be...
A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squ...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squ...
AbstractWe show that the use of generalized multivariable forms of Hermite polynomials provide a use...
AbstractLet γ=0.577215… be the Euler–Mascheroni constant, and let Rn=∑k=1n1k−log(n+12). We prove tha...
In this note we give a short and self-contained proof that, for any δ > 0, ∑_(x≤n≤x+x^δ)λ(n) = o(x^δ...
AbstractIn this note, we present two sufficient conditions for determining the signs of three-term r...
AbstractIn this paper we study generalised prime systems for which the integer counting function NP(...
AbstractIn this work, we study the coefficients of Bazilevic˘ functions and circularly symmetric fun...
AbstractA singular integral equation with a Holderian second member function on [a,b] is considered ...
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