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$\begingroup$ Thanks for your answer! Could you please explain why this result can imply the conclusion? I only know that $h(-d)>0$, which can resolve the case where $f=1$. For this case, according to the answer in the link provided by David E Speyer in comment, it can be proved that when $f=1$, the sum is equal to $\frac{m^2-1}{12}-\frac{S(m)}{2}$. $\endgroup$

Tong Lingling
– Tong Lingling

2025-12-31 01:19:16 +00:00
Commented yesterday
1

$\begingroup$ You are right, it only implies your conjecture for $f=1$, I do not see how to generalize. $\endgroup$

Henri Cohen
– Henri Cohen

2025-12-31 09:13:08 +00:00
Commented yesterday

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