Abstract
We investigate the period function of ∑n=1∞σa(n)e(nz), showing it can be analytically continued to |argz| < π and studying its Taylor series. We use these results to give a simple proof of the Voronoi formula and to prove an exact formula for the second moments of the Riemann zeta function. Moreover, we introduce a family of cotangent sums, functions defined over the rationals, that generalize the Dedekind sum and share with it the property of satisfying a reciprocity formula.
| Translated title of the contribution | Period functiona and cotangent sums |
|---|---|
| Original language | English |
| Pages (from-to) | 215-242 |
| Number of pages | 28 |
| Journal | Algebra and Number Theory |
| Volume | 7 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2013 |