
Re: discriminant of quadratic field relating to a modular sum
Posted:
Oct 3, 2013 5:32 AM


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

