Non-vanishing theta values of characters with special prime conductors

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Guo, Xuejun¹  Peng, Yuzhen² 

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Nanning Normal Univ, Sch Math & Stat, Nanning 530001, Peoples R China

关键词: Theta function;    Dirichlet characters;    Mean values;   

DOI  :  10.1016/j.jmaa.2020.123971

来源: Elsevier

【 摘 要 】

Let p be a prime of the form 2l + 1 or 4l + 1, where l is also a prime. We prove theta(chi, i) not equal 0 for all primitive Dirichlet characters chi with conductor p except for the quadratic and the quartic ones. Our results generalize a theorem of Bengoechea, which asserts theta(chi, i) not equal 0 for non-quadratic chi with large prime conductor p = 2l + 1, where l is also a prime. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free