Minorations de formes linéaires de logarithmes pour les modules de Drinfeld

✍ Scribed by Vincent Bosser

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 339 KB
• Volume: 75
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.1998.2336

✦ Synopsis

Let k=F q (T ), k =F q ((1ÂT)), and let us denote by C the completion of an algebraic closure of k (for the 1ÂT-adic valuation), and by K/C a finite extension of k of degree D. Let (G a , 8 i ) (1 i n) be n Drinfeld modules of rank 1 defined over K (with exponentials e 8 i ), let u 1 , ..., u n # C be such that e 8 i (u i ) # K (1 i n), and let ; 0 , ..., ; n be n+1 elements of K. We obtain in this paper a lower bound for the linear form of logarithms ; 0 +; 1 u 1 + } } } +; n u n (when it is not zero) as a function of the degree D, the heights of the points ; i , the absolute values |u i | and the heights of the e 8 i (u i ), and the heights of the modules (G a , 8 i ).