Artin's L-functions and one-dimensional characters

✍ Scribed by Florin Nicolae

• Book ID: 104024782
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 98 KB
• Volume: 124
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.08.004

✦ Synopsis

Let K/Q be a finite Galois extension with the Galois group G, let χ 1 , . . . , χ r be the irreducible non-trivial characters of G, and let A be the C-algebra generated by the Artin L-functions L(s, χ 1 ), . . . , L(s, χ r ). Let B be the subalgebra of A generated by the L-functions corresponding to induced characters of non-trivial one-dimensional characters of subgroups of G. We prove: (1) B is of Krull dimension r and has the same quotient field as A;