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Fonctions digitales le long des nombres premiers

Bruno Martin, Christian Mauduit, Joël Rivat (2015)

Acta Arithmetica

In a recent work we gave some estimations for exponential sums of the form n x Λ ( n ) e x p ( 2 i π ( f ( n ) + β n ) ) , where Λ denotes the von Mangoldt function, f a digital function, and β a real parameter. The aim of this work is to show how these results can be used to study the statistical properties of digital functions along prime numbers.

Four squares of primes and powers of 2

Lilu Zhao (2014)

Acta Arithmetica

By developing the method of Wooley on the quadratic Waring-Goldbach problem, we prove that all sufficiently large even integers can be expressed as a sum of four squares of primes and 46 powers of 2.

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