The Rankin–Cohen bracket of two Eisenstein series provides a kernel yielding products of the periods of Hecke eigenforms at critical values. Extending this idea leads to a new type of Eisenstein series built with a double sum. We develop the properties of these series and their nonholomorphic analogs and show their connection to values of -functions outside the critical strip.
Nikolaos Diamantis. Cormac O’Sullivan. "Kernels for products of $L$-functions." Algebra Number Theory 7 (8) 1883 - 1917, 2013. https://doi.org/10.2140/ant.2013.7.1883