Counting algebraic points of bounded height on projective spaces

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• 作者：Quentin Guignard¹ ; ^{quentin.guignard@ens.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Heights ; Algebraic points ; Height zeta functions
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：170
• 期：Complete
• 页码：103-141
• 全文大小：539 K

文摘

We prove new estimates on the number of algebraic points of fixed degree and bounded height on projective spaces over a given number field. These results extend previous works of Wolfgang Schmidt [13], Gao Xia [3] and Martin Widmer [18]. Our approach, based on zeta functions, also gives a new proof of Schanuel's theorem.