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Small zeros of additive forms in several variables

✍ Scribed by J. S. Hwang

Book ID: 110557340
Publisher: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year: 1998
Tongue: English
Weight: 377 KB
Volume: 14
Category: Article
ISSN: 1439-7617
DOI: 10.1007/bf02563884

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In this paper it is proved that the pair f =a 1 x k 1 + } } } +a n x k n , g=b 1 x k 1 + } } } + b n x k n , with k= p { ( p&1) k 0 and (k 0 , p)=1, has a common p-adic zero provided n 2k 2+w( p, {) , where w( p, {)=1Â(log p+(1Â{) log( p&1)). It is also proved that if n 2k 2 , then the pair f, g has