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One-level density of zeros of $\Gamma_1(q)$ $L$-functions

math.NT · 2025-12-23 · conditional · novelty 7.0

Extends one-level density support to (-8/3, 8/3) for the unitary family of Gamma_1(q) L-functions under GRH, verifying the Katz-Sarnak prediction and yielding a 62.5% central non-vanishing proportion.

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  • One-level density of zeros of $\Gamma_1(q)$ $L$-functions math.NT · 2025-12-23 · conditional · none · ref 14

    Extends one-level density support to (-8/3, 8/3) for the unitary family of Gamma_1(q) L-functions under GRH, verifying the Katz-Sarnak prediction and yielding a 62.5% central non-vanishing proportion.