July 25th, 2013, 03:24 AM  #1 
Newbie Joined: Jul 2013 Posts: 6 Thanks: 0  Dirichlet characters
Hi! So i have made a table of all the nonprincipal Dirichlet characters mod 16. Is the following table correct? n 1 3 5 7 9 11 13 15 X1(n) 1 1 1 1 1 1 1 1 X2(n) 1 i i 1 1 i i 1 X3(n) 1 1 1 1 1 1 1 1 X4(n) 1 i i 1 1 i i 1 X5(n) 1 1 1 1 1 1 1 1 X6(n) 1 i i 1 1 i i 1 X7(n) 1 1 1 1 1 1 1 1 X8(n) 1 i i 1 1 i i 1 I now want to verify from this table that for each realvalued nonprincipal character X mod 16, that: L(1,X) does not = 0. Any ideas on how to do this? Thanks 
July 25th, 2013, 04:28 AM  #2  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Dirichlet characters Quote:
Quote:
PS : All I have been able to do with elementary analysis that X1, X5 and X7 doesn't work.  
July 25th, 2013, 05:20 AM  #3 
Newbie Joined: Jul 2013 Posts: 6 Thanks: 0  Re: Dirichlet characters
Yeah. I can kinda see that. Iv been trying to research how to tackle this for ages, but their isnt very much information out there on dirichlet characters. It looks as though it should be some simple summation but I cant see what exactly i have to summate

July 25th, 2013, 05:57 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Dirichlet characters Quote:
 
July 25th, 2013, 12:07 PM  #5 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory 
Deleted. A dangerous flaw in the calculation.


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