Results 201 to 210 of about 9,640 (238)

Exponential sums over primes with multiplicative coefficients

Mathematische Zeitschrift, 2023
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Ramaré, Olivier, Viswanadham, G. K.
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EXPONENTIAL SUMS OVER PRIMES IN RESIDUE CLASSES

International Journal of Number Theory, 2010
We specialize a problem studied by Elliott, the behavior of arbitrary sequences ap of complex numbers on residue classes to prime moduli to the case ap = e(αp). For these special cases, we obtain under certain additional conditions improvements on Elliott's results.
Maier, H., Sankaranarayanan, A.
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Short cubic exponential sums over primes

Proceedings of the Steklov Institute of Mathematics, 2017
Vinogradov started the study of short exponential sums over primes of the form \[ \sum\limits_{x ...
Rakhmonov, Z. Kh., Rakhmonov, F. Z.
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Sum of short exponential sums over prime numbers

Doklady Mathematics, 2014
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Rakhmonov, Z. Kh., Rakhmonov, F. Z.
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Exponential sums over primes in short intervals

Science in China Series A, 2006
Let \(\Lambda(m)\) be von Mangoldt's function, \(k \in \mathbb N\), \(2 \leq y \leq x\), and \(\alpha = a/q + \lambda\), with \((a, q) = 1\). In this paper, the authors prove that \[ \begin{multlined} \sum_{x < m \leq x + y} \Lambda(m)\exp(2\pi i\alpha m^k) \ll (qx)^{\epsilon} \Big( yx^{-1/2}(q\Xi)^{1/2} + x^{1/2}q^{1/2}\Xi^{1/6}\\ + y^{1/2}x^{3/10 ...
Liu, Jianya, Lü, Guangshi, Zhan, Tao
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Exponential sums over primes in short intervals

Acta Mathematica Hungarica, 1986
Let \[ S(x,y,\alpha)=\sum_{x ...
A. BALOG, PERELLI, ALBERTO
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Exponential sums over cubes of primes in short intervals and its applications

Mathematische Zeitschrift, 2021
Let \(\Lambda(n)\) be the von Mangoldt function, \(2 \leq y \leq x\), and \(e(z)=e^{2\pi iz}\). In the paper under review the authors obtain bounds for exponential sums over cubes of primes of the form \[ f(\alpha;x,y)=\sum_ ...
Li, Taiyu, Yao, Yanjun
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On exponential sums over primes in short intervals

Monatshefte für Mathematik, 2007
Let \[ S(x,y;\alpha):= \sum_{x< n\leq x+ y} \Lambda(n) e(\alpha n)^2), \] where \(1\leq y\leq x\). For any fixed positive \(A\) and \(\varepsilon\) it is shown that \[ S(x,y;\alpha)= M(x,y;\alpha)+ O_{A,\varepsilon}(y(\log x)^{-A}) \] uniformly for \(x^{2/3+\varepsilon}\leq y\leq x\).
Lü, Guangshi, Lao, Huixue
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Estimation of Exponential Sums over Primes in Short Intervals I

Monatshefte f�r Mathematik, 1999
Let \(\Lambda(n)\) and \(\mu(n)\) be the von Mangoldt and Möbius functions, respectively. A non-trivial estimate for \(\sum_{n\leq x}\Lambda(n)e^{2\pi in\alpha}\), where \(\alpha\) is real, was first obtained by I. M. Vinogradov in his famous solution to the ternary Goldbach problem. Recently much effort has been devoted to such sums over the interval \
Liu, Jianya, Zhan, Tao
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Exponential sums over primes and the prime twin problem

Acta Mathematica Hungarica, 2010
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