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The following arithmetic function is studied by Zagier in connection with values at odd negative integers of zeta functions of real quadratic fields: $$e_r (n)=\sum_{\underset{|x|\leq n}{x^{2}\equiv n\...

I have a puzzle which needs some help form the experts here. Let $d(n)$ be the divisor function, and $d_k(n)$ the $k$-fold divisor function. I) It is known that, for any positive integer $h$, $$d(n+h)...

As I understand things, one of the classical reasons to care about modular forms was their relation to interesting arithmetic functions/counting questions, i.e. on sums of squares and partitions. When ...