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Titlebook: Arithmetical Functions; K. Chandrasekharan Book 1970 Springer-Verlag Berlin · Heidelberg 1970 Arithmetic.Arithmetische Funktion.Prime.func

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发表于 2025-3-21 18:18:38 | 显示全部楼层 |阅读模式
期刊全称Arithmetical Functions
影响因子2023K. Chandrasekharan
视频video
学科分类Grundlehren der mathematischen Wissenschaften
图书封面Titlebook: Arithmetical Functions;  K. Chandrasekharan Book 1970 Springer-Verlag Berlin · Heidelberg 1970 Arithmetic.Arithmetische Funktion.Prime.func
影响因子The plan of this book had its inception in a course of lectures on arithmetical functions given by me in the summer of 1964 at the Forschungsinstitut fUr Mathematik of the Swiss Federal Institute of Technology, Zurich, at the invitation of Professor Beno Eckmann. My Introduction to Analytic Number Theory has appeared in the meanwhile, and this book may be looked upon as a sequel. It presupposes only a modicum of acquaintance with analysis and number theory. The arithmetical functions considered here are those associated with the distribution of prime numbers, as well as the partition function and the divisor function. Some of the problems posed by their asymptotic behaviour form the theme. They afford a glimpse of the variety of analytical methods used in the theory, and of the variety of problems that await solution. I owe a debt of gratitude to Professor Carl Ludwig Siegel, who has read the book in manuscript and given me the benefit of his criticism. I have improved the text in several places in response to his comments. I must thank Professor Raghavan Narasimhan for many stimulating discussions, and Mr. Henri Joris for the valuable assistance he has given me in checking the man
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Persistence and the Data Portal,ry of functions of a complex variable. We shall prove Selberg’s formula in this chapter, and indicate some of its consequences. We shall also prove an inequality due to E. Wirsing, which, when combined with a variant of Selberg’s formula, gives a proof of the prime number theorem.
发表于 2025-3-22 08:35:15 | 显示全部楼层
Expert VB 2008 Business Objects powerful refinement of Weyl’s method was effected by I. M. Vinogradov, who applied it to the solution of a variety of problems in number theory. We shall describe the essentials ofthat method in this chapter, and use it to deduce Chudakov’s refinement of Littlewood’s theorem, to the effect that there exists a constant .>0, such that . t≥t
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,Vinogradov’s method, powerful refinement of Weyl’s method was effected by I. M. Vinogradov, who applied it to the solution of a variety of problems in number theory. We shall describe the essentials ofthat method in this chapter, and use it to deduce Chudakov’s refinement of Littlewood’s theorem, to the effect that there exists a constant .>0, such that . t≥t
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Theorems of Hardy-Ramanujan and of Rademacher on the partition function,
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Book 1970d the book in manuscript and given me the benefit of his criticism. I have improved the text in several places in response to his comments. I must thank Professor Raghavan Narasimhan for many stimulating discussions, and Mr. Henri Joris for the valuable assistance he has given me in checking the man
发表于 2025-3-23 03:00:48 | 显示全部楼层
0072-7830 I must thank Professor Raghavan Narasimhan for many stimulating discussions, and Mr. Henri Joris for the valuable assistance he has given me in checking the man978-3-642-50028-2978-3-642-50026-8Series ISSN 0072-7830 Series E-ISSN 2196-9701
发表于 2025-3-23 08:08:32 | 显示全部楼层
,The prime number theorem and Selberg’s method,ed by Atle Selberg has made a proof of (1) possible without the use of the properties of the zeta-function of Riemann, and without the use of the theory of functions of a complex variable. We shall prove Selberg’s formula in this chapter, and indicate some of its consequences. We shall also prove an
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