2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79601Recently Katz and Sarnak introduced the idea of a symmetry group attached to a family of L-functions, and they gave strong evidence that the symmetry group governs many properties of the distribution of zeros of the L-functions. We consider the mean-values of the L-functions and the mollified mean-square of the L-functions and find evidence that these are also governed by the symmetry group. We use recent work of Keating and Snaith to give a complete description of these mean values. We find a connection to the Barnes-Vignéras $Γ_2$-function and to a family of self-similar functions.23 pages, 6 figuresNumber TheoryMathematical Physics11M06; 11F66; 81Q50text