Approximate functional equation and mean value formula for the derivatives of L-functions attached to cusp forms

2014/02/15 by Yoshikatsu Yashiro, Yashiro, Yoshikatsu
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1402.3716

32 pages

openalex publication_date 2014/02/15 · arxiv created 2015/01/19 · arxiv updated 2015/01/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let f be a holomorphic cusp form of weight k with respect to full modular group SL₂(ℤ) satisfying a normalized Hecke eigenform, L_f(s) the L-function attached to the form f. Good gave the approximate functional equation and mean square formula of L_f(s). In this paper, we shall generalize these formulas for the derivatives of L_f(s).

Citations

• Distribution of zeros and zero-density estimates for the derivatives of L-functions attached to cusp forms

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