Pavel Guerzhoy

Don Zagier suggested a natural construction, which associates a real number and $p$-adic numbers for all primes $p$ to the cusp form $g =
\Delta$ of weight 12. He claimed that these quantities constitute a rational adele. In this paper we prove this
statement, and, more importantly, a similar statement when $g$ is a weight $2$ primitive form with rational integer Fourier coefficients.