Random Diophantine equations, I

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• 作者：Jö ; rg Brü ; dern^a ; ^{bruedern@uni-math.gwdg.de" class="auth_mail} ; Rainer Dietmann^b ; ¹ ; ^{Rainer.Dietmann@rhul.ac.uk" class="auth_mail}
• 关键词：11D72 ; 11E76 ; 11P55
• 刊名：Advances in Mathematics
• 出版年：1 May, 2014
• 年：2014
• 卷：256
• 期：Complete
• 页码：18-45
• 全文大小：408 K

文摘

We consider additive Diophantine equations of degree k in s variables and establish that whenever then almost all such equations satisfy the Hasse principle. The equations that are soluble form a set of positive density, and among the soluble ones almost all equations admit a small solution. Our bound for the smallest solution is nearly best possible.