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- W4211238674 endingPage "193" @default.
- W4211238674 startingPage "131" @default.
- W4211238674 abstract "This chapter starts with a survey of evaluations of exponential sums, and then brings results dealing with the zeta-function and prime number theory. In particular results on differences of consecutive primes are discussed. Certain multiplicative problems, including questions of the existence of consecutive power residues and prime divisors of polynomial values are then presented, and the section on analytic methods ends with information about the circle method, its various applications (problems of Waring, Waring–Kamke and Hilbert–Kamke, …) and the conjectures of Hardy and Littlewood dealing with additive prime number theory. It follows a description of the beginnings of the class-field theory and the related work of Artin as well as the discovery by Hasse of the local-global principle. The main achievements in geometry of numbers and Diophantine approximations of that period include Siegel’s strengthening of Thue’s theorem and Khintchine’s application of measure theory in approximation theory. The chapter ends with a section on Diophantine equations (Siegel’s method and the beginning of modern theory of elliptic curves)." @default.
- W4211238674 created "2022-02-13" @default.
- W4211238674 creator A5073493121 @default.
- W4211238674 date "2012-01-01" @default.
- W4211238674 modified "2023-10-14" @default.
- W4211238674 title "The Twenties" @default.
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