### Abstract

Using the mollifier method, we show that, for a positive proportion of holomorphic Hecke eigenforms of level one and weight bounded by a large enough constant, the associated symmetric square L-function does not vanish at the central point of its critical strip. We note that our proportion is the same as that found by other authors for other families of L-functions also having symplectic symmetry type.

Original language | English |
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Pages (from-to) | 736-762 |

Number of pages | 27 |

Journal | Proceedings of the London Mathematical Society |

Volume | 100 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Non-vanishing of the symmetric square L-function at the central point.** / Khan, Rizwanur.

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*, vol. 100, no. 3, pp. 736-762. https://doi.org/10.1112/plms/pdp048

}

TY - JOUR

T1 - Non-vanishing of the symmetric square L-function at the central point

AU - Khan, Rizwanur

PY - 2010/5

Y1 - 2010/5

N2 - Using the mollifier method, we show that, for a positive proportion of holomorphic Hecke eigenforms of level one and weight bounded by a large enough constant, the associated symmetric square L-function does not vanish at the central point of its critical strip. We note that our proportion is the same as that found by other authors for other families of L-functions also having symplectic symmetry type.

AB - Using the mollifier method, we show that, for a positive proportion of holomorphic Hecke eigenforms of level one and weight bounded by a large enough constant, the associated symmetric square L-function does not vanish at the central point of its critical strip. We note that our proportion is the same as that found by other authors for other families of L-functions also having symplectic symmetry type.

UR - http://www.scopus.com/inward/record.url?scp=77951793327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951793327&partnerID=8YFLogxK

U2 - 10.1112/plms/pdp048

DO - 10.1112/plms/pdp048

M3 - Article

VL - 100

SP - 736

EP - 762

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 3

ER -