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Zakariae.B
Zakariae.B
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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: $$e_r (n)=\sum_{\underset{|x|\leq n}{x^{2}\equiv n\pmod{4}}}\sigma_{r}(\frac{n-x^2}{4}).$$$$e_r (n)=\sum_{\underset{|x|\leq n}{x^{2}\equiv n\pmod{4}}}\sigma_{r}(\frac{n-x^2}{4}),$$ Iwhere $\sigma_r(d)=\sum_{\ell|d}\ell^r$.

I am interested in the $p$-adic behavior of this function. I would like to know whether this function appears elsewhere? Thank you for any suggestions on how to study this function modulo p.

The following arithmetic function is studied by Zagier in connection with values at odd negative integers of zeta functions of real quadratic fields: $$e_r (n)=\sum_{\underset{|x|\leq n}{x^{2}\equiv n\pmod{4}}}\sigma_{r}(\frac{n-x^2}{4}).$$ I am interested in the $p$-adic behavior of this function. I would like to know whether this function appears elsewhere? Thank you for any suggestions on how to study this function modulo p.

The following arithmetic function is studied by Zagier in connection with values at odd negative integers of zeta functions of real quadratic fields: $$e_r (n)=\sum_{\underset{|x|\leq n}{x^{2}\equiv n\pmod{4}}}\sigma_{r}(\frac{n-x^2}{4}),$$ where $\sigma_r(d)=\sum_{\ell|d}\ell^r$.

I am interested in the $p$-adic behavior of this function. I would like to know whether this function appears elsewhere? Thank you for any suggestions on how to study this function modulo p.

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Zakariae.B
Zakariae.B
  • 347
  • 1
  • 6

Where have you encountered the following arithmetic function?

The following arithmetic function is studied by Zagier in connection with values at odd negative integers of zeta functions of real quadratic fields: $$e_r (n)=\sum_{\underset{|x|\leq n}{x^{2}\equiv n\pmod{4}}}\sigma_{r}(\frac{n-x^2}{4}).$$ I am interested in the $p$-adic behavior of this function. I would like to know whether this function appears elsewhere? Thank you for any suggestions on how to study this function modulo p.