The Bettin-Conrey reciprocity theorem and inflated Eulerian polynomials

This thesis is composed of two independent parts. The first part is motivated by\ud a recent paper by Bettin and Conrey, introducing a family of cotangent sums that\ud generalize the classical notion of Dedekind sum and share with it the property of\ud satisfying a reciprocity law. We study particular instances of these arithmetic sums\ud for which it is possible to obtain a simpler reciprocity.\ud The second part focuses on the inflated s-Eulerian polynomial [...], introduced\ud by Pensyl and Savage. We show that [...] is a polynomial\ud for all positive integer sequences s and characterize those sequences s for\ud which the sequence of nonzero coefficients of coincides with that of the\ud polynomial [...]. In particular, we show that all nondecreasing\ud sequences satisfy this condition