An average Chebotarev Density Theorem for generic rank 2 Drinfeld modules with complex multiplication

详细信息    查看全文

• 作者：Alina Carmen Cojocaru^a ; ^b ; ^{cojocaru@math.uic.edu} ; Andrew Michael Shulman^a ; ^{ashulm2@uic.edu}
• 关键词：Drinfeld module ; Weil number ; Density theorem ; Prime distribution
• 刊名：Journal of Number Theory
• 出版年：2013
• 出版时间：March, 2013
• 年：2013
• 卷：133
• 期：3
• 页码：897-914
• 全文大小：244 K

文摘

Let q be an odd prime power and let , . Let ¦× be a Drinfeld A-module over k, of rank 2 and with a non-trivial endomorphism ring. We prove an average effective Chebotarev Density Theorem for the primes splitting completely in the division fields of ¦×, with a very small error term. We also apply our techniques to study the primes of good reduction for ¦× for which the reduced A-module is cyclic.