MOMENT ESTIMATES FOR EXPONENTIAL SUMS OVER k-FREE NUMBERS

Keil, Eugen

doi:10.1142/s1793042112501515

Int. J. Number Theory

2013

DOI: 10.1142/s1793042112501515

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MOMENT ESTIMATES FOR EXPONENTIAL SUMS OVER k-FREE NUMBERS

Eugen Keil

Abstract: Abstract. We investigate the size of L p -integrals for exponential sums over k-free numbers and prove essentially tight bounds.

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Cited by 2 publications

References 9 publications

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Rational points and prime values of polynomials in moderately many variables

Destagnol

Sofos

2019

Bulletin des Sciences Mathématiques

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We derive the Hasse principle and weak approximation for fibrations of certain varieties in the spirit of work by Colliot-Thélène-Sansuc and Harpaz-Skorobogatov-Wittenberg. Our varieties are defined through polynomials in many variables and part of our work is devoted to establishing Schinzel's hypothesis for polynomials of this kind. This last part is achieved by using arguments behind Birch's well-known result regarding the Hasse principle for complete intersections with the notable difference that we prove our result in 50% fewer variables than in the classical Birch setting. We also study the problem of square-free values of an integer polynomial with 66.6% fewer variables than in the Birch setting.

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Rational points and prime values of polynomials in moderately many variables

Destagnol

Sofos

2019

Bulletin des Sciences Mathématiques

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show abstract

Moment estimates for the exponential sum with higher divisor functions

Pandey¹

2022

Comptes Rendus. Mathématique

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MOMENT ESTIMATES FOR EXPONENTIAL SUMS OVER k-FREE NUMBERS

Abstract: Abstract. We investigate the size of L p -integrals for exponential sums over k-free numbers and prove essentially tight bounds.

Cited by 2 publications

References 9 publications

Rational points and prime values of polynomials in moderately many variables

Rational points and prime values of polynomials in moderately many variables

Moment estimates for the exponential sum with higher divisor functions

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