### Abstract

Fix g a Hecke-Maass form for SL _{3}(ℤ). In the family of holomorphic newforms f of fixed weight and large prime level q, we find the average value of the product L(1/2,g × f)L(1/2,f). From this we derive a result on the simultaneous non-vanishing of these L-functions at the central point.

Original language | English |
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Pages (from-to) | 535-553 |

Number of pages | 19 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 152 |

Issue number | 3 |

DOIs | |

Publication status | Published - May 2012 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions.** / Khan, Rizwanur.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions

AU - Khan, Rizwanur

PY - 2012/5

Y1 - 2012/5

N2 - Fix g a Hecke-Maass form for SL 3(ℤ). In the family of holomorphic newforms f of fixed weight and large prime level q, we find the average value of the product L(1/2,g × f)L(1/2,f). From this we derive a result on the simultaneous non-vanishing of these L-functions at the central point.

AB - Fix g a Hecke-Maass form for SL 3(ℤ). In the family of holomorphic newforms f of fixed weight and large prime level q, we find the average value of the product L(1/2,g × f)L(1/2,f). From this we derive a result on the simultaneous non-vanishing of these L-functions at the central point.

UR - http://www.scopus.com/inward/record.url?scp=84860594281&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860594281&partnerID=8YFLogxK

U2 - 10.1017/S0305004111000806

DO - 10.1017/S0305004111000806

M3 - Article

AN - SCOPUS:84860594281

VL - 152

SP - 535

EP - 553

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -