An elementary proof of the Eichler-Selberg trace formula (Q2180847)

The Eichler-Selberg trace formula describes the trace of a Hecke operator on the space modular forms of a given weight in terms of class numbers of binary quadratic forms. Classically, it is derived using (the methods of) the Selberg trace formula, which requires a good amount of analysis. In this nice paper, on the contrary, there is given a purely algebraic proof. By the Eichler-Shimura isomorphism, the space of modular forms is replaced by a space of period polynomials. The key of the proof is the construction of a Hecke operator with special algebraic properties, which imply the trace formula and the Kronecker-Hurwitz class number relation.