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Rademacher on $$J(\tau)$$, Poincaré series of nonpositive weights and the Eichler cohomology. (English) Zbl 0695.10021
A little known paper of H. Rademacher [Am. J. Math. 61, 237-248 (1939; Zbl 0020.22003)] presented a new construction of the modular invariant $$J(\tau)$$. In this expository note the author re-examines this construction from the perspective of a half-century of further advances in the theory of modular and automorphic forms. He gives a clear and concise historical sketch of the main developments in the theory, with special emphasis on Rademacher’s contributions. With the advantage of hindsight, he points out that Eichler cohomology can be viewed as an outgrowth of Rademacher’s work on $$J(\tau)$$.
Reviewer: T.M.Apostol

##### MSC:
 11F03 Modular and automorphic functions 11F67 Special values of automorphic $$L$$-series, periods of automorphic forms, cohomology, modular symbols