Gaps Between Zeros of Automorphic L-functions for GL(2)

Heng Cai TANG

Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 275-286.

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Acta Mathematica Sinica, Chinese Series ›› 2022, Vol. 65 ›› Issue (2) : 275-286. DOI: 10.12386/A2022sxxb0021

Gaps Between Zeros of Automorphic L-functions for GL(2)

  • Heng Cai TANG
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Abstract

Let f(z) be a holomorphic Hecke eigenform of even weight k for the full modular group. L(s, f) is the automorphic L-function associated of f. By the smooth shifted second moment of L(s, f), it is proved that there exist infinitely many consecutive zeros of L(s, f) on the critical line whose gaps are greater than 1.88 times of the averaging spacing.

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cusp form / L-function / mollifier

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Heng Cai TANG. Gaps Between Zeros of Automorphic L-functions for GL(2). Acta Mathematica Sinica, Chinese Series, 2022, 65(2): 275-286 https://doi.org/10.12386/A2022sxxb0021

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