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We formulate a version of the Random Wave Conjecture for the fourth moment ofEisenstein series which is based on Zagier's regularized inner product. Weprove an asymptotic formula expressing the regularized fourth moment as a meanvalue of L-functions. This is an advantage over previous work in theliterature, which has approached the fourth moment problem through truncatedEisenstein series and not yielded a suitable expression in terms ofL-functions.

A conjecture for the regularized fourth moment of Eisenstein series