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One of the most important statistics in studying the zeros of L-functions isthe 1-level density, which measures the concentration of zeros near the centralpoint. Fouvry and Iwaniec [FI] proved that the 1-level density for L-functionsattached to imaginary quadratic fields agrees with results predicted by randommatrix theory. In this paper, we show a similar agreement with random matrixtheory occurring in more general sequences of number fields. We first show thatthe main term agrees with random matrix theory, and similar to all otherfamilies studied to date, is independent of the arithmetic of the fields. Wethen derive the first lower order term of the 1-level density, and see thearithmetic enter.

Low-lying Zeros of Number Field $L$-functions