Results 211 to 220 of about 24,999 (231)

Inequalities between sums over prime numbers in progressions

Research in Number Theory, 2020
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ARITHMETIC SUMS OF LIOUVILLE TYPE OVER RELATIVELY PRIME PAIRS

International Journal of Number Theory, 2012
We prove Liouville's type identities on sums of even integer functions ranging over sets involving relatively prime pairs.
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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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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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A Bombieri–Vinogradov-type result for exponential sums over Piatetski-Shapiro primes

Lithuanian Mathematical Journal, 2022
exaly  

Exponential sums over cubes of primes in short intervals and its applications

Mathematische Zeitschrift, 2021
exaly  

Sums over primes

2004
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Nonlinear sums of characters over primes

Doklady Mathematics, 2008
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SUMS OF CHARACTERS OVER PRIME NUMBERS

Mathematics of the USSR-Izvestiya, 1970
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Oscillations of Cusp Form Coefficients Over Primes

Acta Applicandae Mathematicae, 2008
Qingfeng Sun
exaly