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) for almost all x ∈ [X,2X]. We also sketch a proof of a generalization of such a result to general real-valued multiplicative functions. Both results are special cases of results in our more involved and lengthy recent pre-print
AbstractLet a and b be positive integers and let p be an odd prime such that p=ax2+by2 for some inte...
There are many examples of several variable polynomials whose Mahler measure is expressed in terms o...
AbstractLet σ(n) be the sum of the positive divisors of n, and let A(t) be the natural density of th...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
Let λ denote the Liouville function. A well-known conjecture of Chowla asserts that, for any distinc...
Let $\lambda$ denote the Liouville function. A well known conjecture of Chowla asserts that...
A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squ...
AbstractIn this paper, we reconsider the problem discussed in [G.W. Chen, S.B. Wang, Small amplitude...
AbstractLet γ=0.577215… be the Euler–Mascheroni constant, and let Rn=∑k=1n1k−log(n+12). We prove tha...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squ...
Let $f$ be a measurable function defined on $\mathbb{R}$. For each $n\in\mathbb{Z}$ define the opera...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
AbstractWe investigate the completeness, closure and minimalty of the multiplicity system M(Λ)={tkeλ...
Denote by Ln, N (f, x) a trigonometric polynomial of order at most n possessing the least quadratic...
AbstractLet a and b be positive integers and let p be an odd prime such that p=ax2+by2 for some inte...
There are many examples of several variable polynomials whose Mahler measure is expressed in terms o...
AbstractLet σ(n) be the sum of the positive divisors of n, and let A(t) be the natural density of th...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
Let λ denote the Liouville function. A well-known conjecture of Chowla asserts that, for any distinc...
Let $\lambda$ denote the Liouville function. A well known conjecture of Chowla asserts that...
A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squ...
AbstractIn this paper, we reconsider the problem discussed in [G.W. Chen, S.B. Wang, Small amplitude...
AbstractLet γ=0.577215… be the Euler–Mascheroni constant, and let Rn=∑k=1n1k−log(n+12). We prove tha...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
A direct proof of the resolution of the identity in the odd sector of the Fock space in terms of squ...
Let $f$ be a measurable function defined on $\mathbb{R}$. For each $n\in\mathbb{Z}$ define the opera...
In this paper, on the assumption of the Riemann hypothesis, we give explicit upper bounds on the dif...
AbstractWe investigate the completeness, closure and minimalty of the multiplicity system M(Λ)={tkeλ...
Denote by Ln, N (f, x) a trigonometric polynomial of order at most n possessing the least quadratic...
AbstractLet a and b be positive integers and let p be an odd prime such that p=ax2+by2 for some inte...
There are many examples of several variable polynomials whose Mahler measure is expressed in terms o...
AbstractLet σ(n) be the sum of the positive divisors of n, and let A(t) be the natural density of th...