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Given a formal language L specified in various ways, we consider the problem of determining if L is nonempty. If L is indeed nonempty, we find upper and lower bounds on the length of the shortest string in L.
The Katz-Sarnak Density Conjecture states that the behavior of zeros of a family of L-functions near the central point (as the conductors tend to zero) agrees with the behavior of eigenvalues near 1 of a classical compact group (as the matrix size tends to infinity). Using the Petersson formula, Iwaniec, Luo and Sarnak [ILS] proved that the behavior of… (More)