Journal ArticleMathematische annalen · January 2024
We prove the Manin-Peyre conjecture for the number of rational points of bounded height outside of a thin subset on a family of Fano threefolds of bidegree (1, 2). ...
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Journal ArticleAlgebra and Number Theory · January 1, 2024
Let a polynomial be given. The square sieve can provide an upper bound for the number of integral x ∊ [−B, B]n such that f(x) is a perfect square. Recently this has been generalized substantially: First to a power sieve, counting x ∊ [−B, B]n for which f(x ...
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Journal ArticleAnnali della Scuola Normale Superiore di Pisa - Classe di Scienze · January 1, 2023
We apply a variant of the square-sieve to produce an upper bound for the number of rational points of bounded height on a family of surfaces that admit a fibration over P1 whose general fibre is a hyperelliptic curve. The implied constant does not depend o ...
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Journal ArticleMathematical Proceedings of the Cambridge Philosophical Society · May 1, 2022
Let t: Fp→C be a complex valued function on Fp. A classical problem in analytic number theory is bounding the maximum of the absolute value of the incomplete sums (1/√p)Σ0≤n
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Journal ArticleCompositio Mathematica · July 1, 2021
In this paper, we investigate the distribution of the maximum of partial sums of families of m-periodic complex-valued functions satisfying certain conditions. We obtain precise uniform estimates for the distribution function of this maximum in a near-opti ...
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Journal ArticleInternational Mathematics Research Notices · January 1, 2021
Let $f\in \mathbb{Z}[T]$ be any polynomial of degree $d>1$ and $F\in \mathbb{Z}[X-{0},..,X-{n}]$ an irreducible homogeneous polynomial of degree $e>1$ such that the projective hypersurface $V(F)$ is smooth. In this paper we present a new bound for $N(f,F,B ...
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