A prime number theorem in short intervals for dihedral Maass newforms

被引：0
作者：
Guan, Bin [1 ]
机构：
[1] Shandong Univ, Data Sci Inst, 27 Shanda South Rd, Jinan 250100, Peoples R China
来源：
AIMS MATHEMATICS | 2024年 / 9卷 / 02期
关键词：
prime number theorem; Hecke eigenvalue; Rankin-Selberg L-function; zero-free region; zero density estimate; ZEROS;
D O I：
10.3934/math.2024238
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove a prime number theorem in short intervals for the Rankin-Selberg L-function L(s, phi x phi), where phi is a fixed dihedral Maass newform. As an application, we give a lower bound for the proportion of primes in a short interval at which the Hecke eigenvalues of the dihedral form are greater than a given constant.
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收藏
页码：4896 / 4906
页数：11
相关论文
共 22 条
  • [1] Bump Daniel., 1997, Automorphic Forms and Representations, DOI [DOI 10.1017/CBO9780511609572, 10.1017/CBO9780511609572]
  • [2] Watson TC, 2008, Arxiv, DOI arXiv:0810.0425
  • [3] A ZERO-FREE REGION FOR THE HECKE L-FUNCTIONS
    COLEMAN, MD
    [J]. MATHEMATIKA, 1990, 37 (74) : 287 - 304
  • [4] Godement R., 1972, ZETA FUNCTIONS SIMPL, V260, DOI [10.1007/BFb0070263, https://doi.org/10.1007/BFb0070263, DOI 10.1007/BFB0070263]
  • [5] Hoffstein J., 1995, INT MATH RES NOTICES, V1995, P279
  • [6] QUANTUM VARIANCE FOR DIHEDRAL MAASS FORMS
    Huang, Bingrong
    Lester, Stephen
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2023, 376 (01) : 643 - 695
  • [7] TOWARDS A GLn VARIANT OF THE HOHEISEL PHENOMENON
    Humphries, Peter
    Thorner, Jesse
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 375 (03) : 1801 - 1824
  • [8] On the Random Wave Conjecture for Dihedral Maass Forms
    Humphries, Peter
    Khan, Rizwanur
    [J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2020, 30 (01) : 34 - 125
  • [9] HUXLEY MN, 1972, INVENT MATH, V15, P164
  • [10] Ingham A. E., 1940, Quart. J. Math. Oxford Ser., V11, P291
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