Results 211 to 220 of about 9,640 (238)

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

The Ramanujan Journal, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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American Cancer Society nutrition and physical activity guideline for cancer survivors

Ca-A Cancer Journal for Clinicians, 2022
Cheryl L Rock, Cynthia A Thomson, Marian L Neuhouser   +2 more
exaly  

Cancer statistics, 2020

Ca-A Cancer Journal for Clinicians, 2020
Rebecca L Siegel, Kimberly D Miller
exaly  

Treatment of muscle‐invasive and advanced bladder cancer in 2020

Ca-A Cancer Journal for Clinicians, 2020
Vaibhav G Patel, William K Oh, Matthew D Galsky   +2 more
exaly