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We prove several results on the distribution of values of  L ‐functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we study families of symmetric power  L ‐functions of holomorphic cusp forms in the level aspect (assuming the automorphy of these  L ‐functions) at  s  = 1, functions in the Selberg class (in the height aspect) and quadratic twists of a fixed GL( m )/ℚ‐automorphic cusp form at  s  = 1.

Distribution of values of L ‐functions at the edge of the critical strip