林德勒夫猜想
註解和參考資料

↑  參見Lindelöf (1908)
↑  Lindelöf (1908)
↑  Hardy, G. H.; Littlewood, J. E. . Proc. R. Soc. A. 1923: 403–412.
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↑  Titchmarsh, E. C. . The Quarterly Journal of Mathematics. 1932, os–3 (1): 133–141. ISSN 0033-5606. doi:10.1093/qmath/os-3.1.133.
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↑  Titchmarsh, E. C. . The Quarterly Journal of Mathematics. 1942, os–13 (1): 11–17. ISSN 0033-5606. doi:10.1093/qmath/os-13.1.11.
↑  Min, Szu-Hoa. . Transactions of the American Mathematical Society. 1949, 65 (3): 448–472. ISSN 0002-9947. doi:10.1090/S0002-9947-1949-0030996-6.
↑  Haneke, W. . Acta Arithmetica. 1963, 8 (4): 357–430. ISSN 0065-1036. doi:10.4064/aa-8-4-357-430 （German）.  引文格式1维护：未识别语文类型 (link)
↑  Kolesnik, G. A. . Acta Arithmetica. 1973, 25 (1): 7–30  [2024-02-05]. ISSN 0065-1036 （Russian）.  引文格式1维护：未识别语文类型 (link)
↑  Kolesnik, Grigori. . Pacific Journal of Mathematics. 1982-01-01, 98 (1): 107–122. ISSN 0030-8730. doi:10.2140/pjm.1982.98.107.
↑  Kolesnik, G. . Acta Arithmetica. 1985, 45 (2): 115–143. doi:10.4064/aa-45-2-115-143.
↑  Bombieri, E.; Iwaniec, H. . Annali della Scuola Normale Superiore di Pisa - Classe di Scienze. 1986, 13 (3): 449–472.
↑  Huxley (2002), Huxley (2005)
↑  Bourgain (2017)
↑  Bourgain (2017)
↑  Backlund (1918–1919)
↑  Heath-Brown (1979)
↑  Ingham (1928)
↑  Conrey & Ghosh (1998)
↑  Keating & Snaith (2000)
↑  Cramér, Harald. . Acta Arithmetica. 1936, 2 (1): 23–46. ISSN 0065-1036. doi:10.4064/aa-2-1-23-46.
↑  Banks, William; Ford, Kevin; Tao, Terence. . Inventiones Mathematicae. 2023, 233 (3): 1471–1518. ISSN 0020-9910. arXiv:1908.08613 . doi:10.1007/s00222-023-01199-0.
↑  Trudgian, Timothy S.; Yang, Andrew. . 2023. arXiv:2306.05599  [math.NT].
↑  . aimath.org.   [2024-07-16].
↑  . encyclopediaofmath.org.   [2024-07-16].
↑  . www.ias.edu. 2024-06-04  [2024-07-16] （英语）.
↑  . www.ias.edu. 2024-06-04  [2024-07-16] （英语）.
↑  Ingham, A. E. . The Quarterly Journal of Mathematics. 1940, os–11 (1): 201–202. ISSN 0033-5606. doi:10.1093/qmath/os-11.1.201 （英语）.
↑  Huxley, M. N. . Inventiones Mathematicae. 1971, 15 (2): 164–170. ISSN 0020-9910. doi:10.1007/BF01418933.
↑  Guth, Larry; Maynard, James. . 2024. arXiv:2405.20552  [math.NT].
↑  Bischoff, Manon. . Scientific American.   [2024-07-16] （英语）.
↑  Cepelewicz, Jordana. . Quanta Magazine. 2024-07-15  [2024-07-16] （英语）.
↑  Bernstein, Joseph; Reznikov, Andre. . Annals of Mathematics. 2010-10-05, 172 (3): 1679–1718. ISSN 0003-486X. S2CID 14745024. arXiv:math/0608555 . doi:10.4007/annals.2010.172.1679  （英语）.
↑  Michel, Philippe; Venkatesh, Akshay. . Publications Mathématiques de l'IHÉS. 2010, 111 (1): 171–271. CiteSeerX 10.1.1.750.8950 . S2CID 14155294. arXiv:0903.3591 . doi:10.1007/s10240-010-0025-8.
↑  Nelson, Paul D. . 2021-09-30. arXiv:2109.15230  [math.NT].
↑  Hartnett, Kevin. . Quanta Magazine. 2022-01-13  [2022-02-17] （英语）.
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|  论 编數論中的L函數 |
| --- | --- |
解析例子:  黎曼ζ函數  狄利克雷L函數  赫克特徵的L函數（英语：）  自守L函數（英语：）  塞爾伯格類（英语：） 
代數例子:  戴德金ζ函數（英语：）  阿廷L函數（英语：）  哈斯-韋伊L函數（英语：）  原動L函數（英语：） 
定理:  類數公式  黎曼-馮·曼戈爾特公式（英语：）  韋伊猜想（英语：） 
解析猜想:  黎曼猜想  廣義黎曼猜想  林德勒夫猜想  拉馬努金-皮特森猜想（英语：）  阿廷L函數猜想（英语：） 
代數猜想:  貝赫和斯維訥通-戴爾猜想  L函數的特殊值（英语：）  朗蘭茲猜想 
p進L函數（英语：）:  岩澤理論的主猜想（英语：）  塞爾瑪群（英语：）  歐拉系統（英语：） 
已知的無零點區域，略合於此張圖的右下角；而若黎曼猜想得證，就會將整張圖給壓縮到x軸上，也就是 A_{RH}(\sigma >1/2)=0。在另一邊，此圖中的上界 A_{DH}(1-\sigma )=2(1-1/2)=1與從黎曼-馮·曼戈爾特公式（英语：）得出的顯著上界相合。（也有其他各式各樣的估計）