Results 191 to 200 of about 261 (203)

On Averages of Exponential Sums over Primes

1987
In this paper we shall be concerned with obtaining approximations to and estimates for the sum $${{\text{S}}_{\text{N}}}(\alpha ){\text{ = }}\sum\limits_{{\text{n}} \leqslant {\text{N}}} {{\text{e}}({\text{n}}\alpha ) \wedge {\text{(n)}}}$$ where e(x) = exp(2πix), α is real, and Λ(n) is the von Mangoldt function.
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The L ¹ mean of Exponential Sums over Primes

Bulletin of the London Mathematical Society, 1988
The author investigates the behaviour of the \(L^ 1\)-mean \(\int^{1}_{0}| S(x)| dx\) of the exponential sum \(S(x) = \sum_{n\leq X}\Lambda(n)e^{2\pi inx}\), where \(\Lambda\) is von Mangoldt's function. Such means often arise in investigations in analytic number theory.
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Exponential sum estimates over subgroups and almost subgroups of $$ \mathbb{Z}_{Q}^{*} $$ , where Q is composite with few prime factors

GAFA Geometric And Functional Analysis, 2006
In this paper we extend the exponential sum results from [BK] and [BGK] for prime moduli to composite moduli q involving a bounded number of prime factors. In particular, we obtain nontrivial bounds on the exponential sums associated to multiplicative subgroups H of size qδ, for any given δ >  0.
J. Bourgain, M. -C. Chang
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Effective estimates of exponential sums over primes

1996
The asymptotic behavior of the sum $$S(x,\alpha ) = \sum\limits_{n \leqslant x} {\pi (n)e(n\alpha ),}$$ where α is real, e(α) = e2πiα, and Λ is the von Mangoldt function, has been extensively studied by many authors. It plays a central role in Vinogradov’s solution of the 3-primes conjecture [10].
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Exponential sums over primes formed with coefficients of primitive cusp forms

Acta Mathematica Sinica, English Series, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the representation of large integers as sums of four almost equal squares of primes

Ramanujan Journal, 2007
Wenguang Zhai, Guangshi Lu
exaly  

Sums of primes and squares of primes in short intervals

Monatshefte Fur Mathematik, 2008
Angel Kumchev
exaly  

EXPONENTIAL SUMS OVER POINTS OF ELLIPTIC CURVES WITH RECIPROCALS OF PRIMES

Mathematika, 2012
Alina Ostafe, Igor Shparlinski
exaly  

ON EXPONENTIAL SUMS INVOLVING COEFFICIENTS OFL-FUNCTIONS FOR SL(3, ℤ) OVER PRIMES

The Quarterly Journal of Mathematics, 2016
Fei Hou, Yujiao Jiang, Guangshi Lü
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Barban–Davenport–Halberstam Type Theorems for Exponential Sums and Piatetski-Shapiro Primes

Results in Mathematics
S I Dimitrov, Dimitrov S I
exaly