Add to ORKGLet $\gamma<1<c$ and $19(c-1)+171(1-\gamma)<9$. In this paper, we establish an asymptotic formula for exponential sums over Piatetski-Shapiro primes $p=[n^{1/\gamma}]$ in arithmetic progressions
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
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...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
We develop a technique to compute asymptotic expansions for recurrent sequences of the form an+1 = f...
By introducing multi-parameters and conjugate exponents and using Euler-Maclaurin’s summation formul...
By introducing multi-parameters and conjugate exponents and using Euler-Maclaurin’s summation formul...
In the paper, by virtue of the convolution theorem for the Laplace transforms, with the aid of three...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
AbstractRecently, R. Tauraso established finite p-analogues of Apéryʼs famous series for ζ(2) and ζ(...
We give nontrivial bounds in various ranges for character sums of the form ∑n S(x,y) χ(R1(n))eq(R2...
Let $\omega^*(n)$ be the number of primes $p$ such that $p-1$ divides $n$. In 1955, Prachar proved t...
AbstractLet a and b be positive integers and let p be an odd prime such that p=ax2+by2 for some inte...
AbstractLet γ=0.577215… be the Euler–Mascheroni constant, and let Rn=∑k=1n1k−log(n+12). We prove tha...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
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...
AbstractWe use the explicit formula of V. Shevelev for the best possible exponent α(m) in the error ...
We develop a technique to compute asymptotic expansions for recurrent sequences of the form an+1 = f...
By introducing multi-parameters and conjugate exponents and using Euler-Maclaurin’s summation formul...
By introducing multi-parameters and conjugate exponents and using Euler-Maclaurin’s summation formul...
In the paper, by virtue of the convolution theorem for the Laplace transforms, with the aid of three...
Contains a correction with respect to the printed versionWe provide sharp estimates for the number o...
An improved estimate is given for |θ (x) − x|, where θ (x) = p≤x log p. Four applications are give...
AbstractRecently, R. Tauraso established finite p-analogues of Apéryʼs famous series for ζ(2) and ζ(...
We give nontrivial bounds in various ranges for character sums of the form ∑n S(x,y) χ(R1(n))eq(R2...
Let $\omega^*(n)$ be the number of primes $p$ such that $p-1$ divides $n$. In 1955, Prachar proved t...
AbstractLet a and b be positive integers and let p be an odd prime such that p=ax2+by2 for some inte...
AbstractLet γ=0.577215… be the Euler–Mascheroni constant, and let Rn=∑k=1n1k−log(n+12). We prove tha...
Let \u3c8K be the Chebyshev function of a number field K. Let \u3c8K(1)(x) := 2b0x\u3c8K(t) dt and \...
AbstractWe prove that for any nonnegative integers n and r the binomial sum∑k=−nn(2nn−k)k2r is divis...
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...