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Topic: discriminant of quadratic field relating to a modular sum
Replies: 12   Last Post: Oct 3, 2013 5:32 AM

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Leon Aigret

Posts: 31
Registered: 12/2/12
Re: discriminant of quadratic field relating to a modular sum
Posted: Oct 3, 2013 5:32 AM
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On Sat, 28 Sep 2013 07:21:57 -0700 (PDT), oferbarasofsky@gmail.com
replied to quasi with:

>
>> But in any case, as far as I can see, the answer has really
>> nothing to do with discriminants of quadratic fields. The
>> connection is only incidental. It's just a question of whether
>> M_2(n) = 0 mod 2n for all n.

>
>Again, you are correct in all your assumptions of "what I meant".
>
>Perhaps you are right about "nothing to do with discriminants of
>quadratic fields", but then the data shows that if n is some
>power of 2 > 2, then 2 * M_2(n) / D(n) = Some power of 2.
>
>For example:
>
>(n=4) 2*M_2(4) / D(4) = 4
>(n=4) 16 / 4 = 4
>
>(n=8) 2*M_2(8) / D(8) = 16
>(n=8) 128 / 8 = 16
>
>(n=16) 2*M_2(16) / D(16) = 256
>(n=16) 1024 / 4 = 256
>
>(n=32) 2*M_2(32) / D(32) = 2048
>(n=32) 16384 / 8 = 2048
>
>(n=64) 2*M_2(64) / D(64) = 32768
>(n=64) 131072 / 4 = 32768


However, M_2(256) = 5767168, M_2(512) = 46137344 and
M_2(1024) = 369098752 are all divisible by 11.

Leon



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