Some highlights from the history of probabilistic number theory

机译：概率数字理论史上的一些亮点

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In this survey lecture it is intended to sketch some parts [chosenaccording to the author's interests] of the [early] history of Probabilis-tic Number Theory, beginning with PAUL TURANS proof (1934) of theHARDY—RAMANUJAN result on the "normal order" of the additive func-tion w(n), the ERDOS—WINTNER Theorem, and the ERDOs-KAc The-orem. Next, mean-value theorems for arithmetical functions, and theKUBILIUS model and its application to limit laws for additive functionswill be described in short. Subsuming applications of the theory of almost-periodic functionsunder the concept of "Probabilistic Number Theory", the problemof "uniformly-almost-even functions with prescribed values" will besketched, and the KNOPFMACHER — SCHWARZ — SPILKER theory ofintegration of arithmetical functions will be sketched. Next, K.-H.INDLEKOFERs elegant theory of integration of functions N C of willbe described. Finally, it is tried to scratch the surface of the topic "universality",where important contributions came from the university of Vilnius.

机译：在本调查讲座中，旨在绘制[早期]概率的概率[早期]概率[早期]的概率[早期]概率，从保罗··罗拉曼·武兰师（1934年）开始了“正常秩序”添加剂函数 - TiOn W（n），鄂尔多斯 - Wintner定理和厄尔多斯 - kac的orem。接下来，简称，简要介绍了算术功能的平均值定理，以及kubilius模型及其限制附加功能规律的应用。 “概率数字理论”概念中的近似周期函数理论的综合应用程序，“统一 - 几乎 - 甚至与规定值的统一函数”将被勾勒出来的克劳赫 - 施瓦茨 - 斯普尔克·斯普利克理论将进行速写。接下来，K.-H.Indlekofers优雅的函数集成理论N CWBE描述。最后，试图划伤主题“普遍性”的表面，其中重要贡献来自维尔纽斯大学。

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《International Conference on Probability and Number Theory》|2007年||共53页
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作者
Wolfgang Schwarz;
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中图分类 O211-532;
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probabilistic number theory; history;

机译：概率数字理论;历史;

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Gustav and KnightS. (eds), British Industrial Fictions , University of Wales Press, 2000, pp. viii + 212, £14.99 pb.; BalchJack S., Lamps at High Noon , University of Illinois Press, 2000, pp. xl + 404, $19.45 pb.; ConroyJack, A World to Win , University of Illinois Press, 2000, pp. xxxv + 348, $17.95 pb.GagnierRegenia, The Insatiability of Human Wants: Economics and Aesthetics in Market Society , University of Chicago Press, 2000, pp. 352, £10.50 pb. [O] . Paul Hyland, R. C. Richardson, Ivan Roots, 2001

机译：点评：历史的研究：一个书目指南，历史的英语理念从柯勒律治到科林伍德，英国当地历史，亚瑟和他的英语变脸：亚瑟王传说中中世纪英国生活和文学，在英国文艺复兴时期颁布性别舞台上，莎士比亚的女性结局，写英文共和国：诗歌，修辞学和政治学1627年至1660年，对旧的新故事：在小说中，天主教和反天主教在早期现代英语文本，长子继承权和继承权在英国圣经模式：综述文学中的历史和代表，通过对小说恢复的英语内战：一个注释的参考书目，戴安娜，自我利益和英国国家身份，古人与现代人之间的古典罗马的痕迹和古典罗马：巴洛克文化在恢复英格兰，浪漫英格兰的Bacchus：1780-1830，厌恶经济学的作家和饮料：十八世纪的文学业务ritain，伪造的房子在十八世纪的英国，穿着我们的衣服，牛津伴侣的浪漫时代：英国文化，1776 - 1832，国内空间：阅读十九世纪的内部，维多利亚人理论上：从德里达到布朗，美德的年龄：英国文化从恢复到浪漫主义，悲惨的痛苦：维多利亚州的残疾和感情，妇女作家第一次世界大战：一个注释的书目，文学中的酒吧，英国工业小说，人类的缘故想要：市场苏格里希第德森市场的经济和美学。 C.，历史的研究：一个书目指南，第二版，曼彻斯特大学出版社，2000，第十四+ 140，£40.00.ParkerChristopher，历史的英语从理念到柯勒律治科林伍德，Ashgate出版社，2000，页。 VII + 244，£45.Richardsonr。 C.（ed。），英语当地历史的变化面孔，ashgate，2000，pp。viii + 218，£45.00.00.00.Parronw。 RJ（编辑），亚瑟和他的英文：亚瑟王传说中中世纪英国生活和文学，威尔士出版社，1999年大学，第398，£35.00.ComensoliViviana和RussellAnne（EDS），英国文艺复兴舞台上颁布性别，伊利诺伊大学出版社，1999，第270页，18.95英镑; SaunderseVe Rachel，在早期现代英格兰舞台上的雷切尔，性别和识字，剑桥大学出版社，1999，PP。260，£35.BerringPhilippa，莎士比亚的女性化的遗址，Routledge，1999，PP。197，£15.99 PB。 Bellilona，伊丽莎白裔女性和甲师诗歌，剑桥大学出版社，1998，PP。262，£35.00.norbrookdavid，写英国共和国：诗歌，修辞和政治1627-1660，剑桥大学出版社，1999，PP。XIII + 509 ，£40.FischHarold，对于旧的新故事：在小说，Macmillan出版社，1998年，第圣经模式X + 236，£42.50; Fischharold，Shakespeare，Milton和Blake的圣经存在，1999年，PP。Xi + 330，£45.marottiarthur F.（Ed。），天主教和早期现代英语文本，Macmillan，1999，PP的天主教和反天主教。XVII + 266，£47.50; Shellalison，天主教，争议和英国文学想象，1558-1660，剑桥大学出版社，1999，PP。XI + 309，£37.50.Jamoussizouheir，Punigoghts和Envland在英国：他们在文学中的历史和代表调查，中心出版大学，突尼斯，1999，PP。293,8 DT.Murphorn Xane C.，英语内战通过虚构的恢复：一个注释书目，格林伍德出版社，韦斯特波特，CT，CT。，2000，PP。VIII + 349，£63.95 .HammondPaul，德莱顿和古典罗马，克拉伦登出版社，牛津，1999年的痕迹，第305，£45.00.LevineJoseph M.，古人和现代人之间：巴洛克文化恢复英格兰，耶鲁大学出版社，1999，页。 XIV + 279，£27.50.50.50.5.50.Tayloranya，浪漫英格兰的Bacchus：作家和饮料，1780-1830，Macmillan，1999，PP。Xi + 264，£47.50.Mandelllaura，罕有内容：十八世纪英国的文学业务，肯塔基州大学，1999，PP。X + 228，$ 42.00.Bainespaul，在十八世纪的英国伪造之家，阿什捷，1999年，PP。第八次+ 195，£47.50.50.50.50.Munnsjessica和Richardspenny（EDS），穿着我们，纽瓦克，特拉华大学出版社，1999，PP。362，£ 37.McCalmanIain（编辑），牛津伴侣对浪漫的年龄：英国文化，1776年至1832年，牛津大学出版社，1999，页。 XII + 780，£85.Brydeninga和Floydjanet（EDS），国内空间：阅读十九世纪内部，曼彻斯特大学出版社，1999，PP。XII + 219，£40.00; KiddAlan和NichollsDavid（EDS），性别，公民文化和消费：在英国，1800年至1940年中产阶层的身份，曼彻斯特大学出版社，1999年，第十四+ 223，£46.00，PB。 14.99英镑的理论上，从Derrida到Browning，曼彻斯特大学出版社，1999年，PP。X + 180，£40.Moreedavid，富于浪漫主义，2000，2000，PP。八+ 330，£45.Klesmary，悲惨的痛苦：宾夕法尼亚大学的维多利亚州美国的残疾和感情，1999年，第211次，第一次第一次世界大战的妇女作家：一名注册参考书目，rutledge，2000，pp。230，75英镑; TyleeClaire与Turnerelaine和Cardinalagnes（EDS），战争扮演妇女：国际选集，Routledge，2000，PP。225，£16.99 PB.Taylorjohn A.，戴安娜，自身利益和英国国家身份，Praeger，2000，PP 。169，£44.95.EARNShawsteven，文学中的酒吧，曼彻斯特大学出版社，2000，PP。X + 294，£45和15.99英镑PB.Klaush。古斯塔夫和骑士。（EDS），英国工业小说，威尔士大学出版社，2000，PP。VIII + 212，£14.99 PB。 Balchjack S.，伊利诺伊大学高中中午的灯，2000年，PP。XL + 404，$ 19.45 PB。康罗伊士队，伊利诺伊大学的世界胜利，2000年，PP。XXXV + 348，17.95磅PB.Gagnierregenia，人类想要的缘故：市场学会的经济学和美学，芝加哥大学出版社，2000，PP。352，£ 10.50 PB。

Some highlights from the history of probabilistic number theory

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