Results 181 to 190 of about 261 (203)

On exponential sums over primes in short intervals

Monatshefte Fur 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 \(x^{2/3+\varepsilon}\leq y\leq x\).
Guangshi Lu
exaly   +3 more sources

Exponential sums over primes in short intervals

Acta Mathematica Hungarica, 1986
Let \[ S(x,y,\alpha)=\sum_{x ...
A Balog, Balog A, A Perelli
exaly   +3 more sources

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.
exaly   +3 more sources

Bombieri-type theorems for exponential sums over primes in short intervals and its application

Ramanujan Journal, 2017
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Exponential sums over primes with multiplicative coefficients

Mathematische Zeitschrift, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ramaré, Olivier, Viswanadham, G. K.
openaire   +2 more sources

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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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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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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An Exponential Sum Over Primes

2017
In additive prime number theory the starting point of many investigations is the generating function (1) S ( α )
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