Estimation de sommes multiples de fonctions arithmétiques

Régis de la Bretèche

doi:10.1023/A:1011803816545

Abstract

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We estimate some sums of the shape S(Xβ1,…, Xβm): = [sum ]1 [les ] d1 [les ] Xβ1… [sum ]1 [les ] dm [les ] Xβm ƒ(d1,…, dm), when m ∈ $\Bbb N$ and f is a nonnegative arithmetical function. We relate them to the behaviour of the associated Dirichlet series

F(s1,…, sm) = ∞[sum ]d1 = 1 … ∞[sum ]dm = 1 f(d1,…, dm)/d1s1 … dmsm. The main aim of this work is to develop analytic tools to count the rational points of bounded height on toric varieties.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Bhowmik, Gautami Essouabri, Driss and Lichtin, Ben 2007. Meromorphic continuation of multivariable Euler products. Forum Mathematicum, Vol. 19, Issue. 6,

Chandee, Vorrapan and Li, Xiannan 2013. Lower Bounds for Small Fractional Moments of Dirichlet L-Functions. International Mathematics Research Notices, Vol. 2013, Issue. 19, p. 4349.

Durand, Arnaud and Jaffard, Stéphane 2013. Further Developments in Fractals and Related Fields. p. 63.

Harper, Adam J. Nikeghbali, Ashkan and Radziwiłł, Maksym 2015. Analytic Number Theory. p. 145.

Munsch, Marc and Shparlinski, Igor E. 2016. UPPER AND LOWER BOUNDS FOR HIGHER MOMENTS OF THETA FUNCTIONS. The Quarterly Journal of Mathematics, Vol. 67, Issue. 1, p. 53.

Pieropan, Marta 2016. Imaginary quadratic points on toric varieties via universal torsors. Manuscripta Mathematica, Vol. 150, Issue. 3-4, p. 415.

Onozuka, Tomokazu 2017. The multiple Dirichlet product and the multiple Dirichlet series. International Journal of Number Theory, Vol. 13, Issue. 08, p. 2181.

Bettin, Sandro and Destagnol, Kevin 2019. THE POWER‐SAVING MANIN–PEYRE CONJECTURE FOR A SENARY CUBIC. Mathematika, Vol. 65, Issue. 4, p. 789.

de la Bretèche, Régis Destagnol, Kevin Liu, Jianya Wu, Jie and Zhao, Yongqiang 2019. On a certain non-split cubic surface. Science China Mathematics, Vol. 62, Issue. 12, p. 2435.

Matsumoto, Kohji Nawashiro, Akihiko and Tsumura, Hirofumi 2021. Double Dirichlet series associated with arithmetic functions. Kodai Mathematical Journal, Vol. 44, Issue. 3,

Matsumoto, Kohji 2021. A Survey on the Theory of Multiple Dirichlet Series with Arithmetical Coefficients as Numerators. Lithuanian Mathematical Journal, Vol. 61, Issue. 3, p. 391.

de la Bretèche, Régis Kurlberg, Pär and Shparlinski, Igor E 2021. On the Number of Products Which Form Perfect Powers and Discriminants of Multiquadratic Extensions. International Mathematics Research Notices, Vol. 2021, Issue. 22, p. 17140.

Demirhan, Arda and Takloo-Bighash, Ramin 2022. Distribution of rational points on toric varieties: all the heights. Research in the Mathematical Sciences, Vol. 9, Issue. 4,

Essouabri, Driss Salinas Zavala, Christoper and Tóth, László 2022. Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function. Journal of Number Theory, Vol. 236, Issue. , p. 404.

Kim, Sungjin 2022. On the reciprocal sum of lcm of k-tuples. Research in Number Theory, Vol. 8, Issue. 3,

Heyman, Randell and Tóth, László 2023. Number Theory in Memory of Eduard Wirsing. p. 157.

Pieropan, Marta and Schindler, Damaris 2023. Hyperbola method on toric varieties. Journal de l’École polytechnique — Mathématiques, Vol. 11, Issue. , p. 107.

Chinta, Gautam Kaplan, Nathan and Koplewitz, Shaked 2023. The cotype zeta function of Zd. Indagationes Mathematicae, Vol. 34, Issue. 3, p. 643.

Wang, Victor Y. and Xu, Max Wenqiang 2024. Paucity phenomena for polynomial products. Bulletin of the London Mathematical Society, Vol. 56, Issue. 8, p. 2718.

Pandey, Mayank Wang, Victor Y. and Xu, Max Wenqiang 2024. Partial sums of typical multiplicative functions over short moving intervals. Algebra & Number Theory, Vol. 18, Issue. 2, p. 389.

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Estimation de sommes multiples de fonctions arithmétiques

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Estimation de sommes multiples de fonctions arithmétiques

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