Munshi, Ritabrata
(2011)
*On mean values and non-vanishing of derivatives of L-functions in a nonlinear family*
Compositio Mathematica, 147
(01).
pp. 19-34.
ISSN 0010-437X

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Official URL: https://www.cambridge.org/core/journals/compositio...

Related URL: http://dx.doi.org/10.1112/S0010437X10004732

## Abstract

We prove a mean-value result for derivatives of L-functions at the center of the critical strip for a family of forms obtained by twisting a fixed form by quadratic characters with modulus which can be represented as sum of two squares. Such a family of forms is related to elliptic fibrations given by the equation q(t)y^{2}=f(x) where q(t)=t^{2}+1 and f(x) is a cubic polynomial. The aim of the paper is to establish a prototype result for such quadratic families. Though our method can be generalized to prove similar results for any positive definite quadratic form in place of sum of two squares, we refrain from doing so to keep the presentation as clear as possible.

Item Type: | Article |
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Source: | Copyright of this article belongs to Foundation Compositio Mathematica. |

ID Code: | 110829 |

Deposited On: | 31 Jan 2018 09:08 |

Last Modified: | 31 Jan 2018 09:08 |

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