Period functions and cotangent sums

Details Period functions and cotangent sums Period functions and cotangent sums

2011-11-03

arxiv.org/abs/1111.0931v1

Mathematics

Number Theory

32 pages, 5 figures

Scientific paper

We investigate the period function of $\sum_{n=1}^\infty\sigma_a(n)\e{nz}$, showing it can be analytically continued to $|\arg z|<\pi$ 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. In particular, we find a reciprocity formula for the Vasyunin sum.

Affiliated with

Also associated with

No associations

Rating

Period functions and cotangent sums does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Period functions and cotangent sums, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Period functions and cotangent sums will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-703348