Titlebook: Arithmetic Tales; Advanced Edition Olivier Bordellès Textbook 2020Latest edition Springer Nature Switzerland AG 2020 arithmetical functions

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Prime Numbers,In this chapter, elementary and non-elementary methods to investigate the distribution of prime numbers are given: Chebyshev’s estimates, Mertens’s theorems, the Prime Number Theorem, a complete study of the Riemann zeta-function and the Dirichlet .-functions, the Riemann hypothesis and its consequences.

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Lattice Points,This chapter is devoted to the study of integer points close to smooth curves, involved among other things in the problem of estimating certain multiplicative functions in short intervals. The chapter focuses on elementary methods resting on divided differences and some combinatorial tools.

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Textbook 2020Latest edition others. Throughout the book, the emphasis is on explicit results..Assuming only familiarity with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exe

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0172-5939 ty with elementary number theory and analysis at an undergraduate level, this textbook provides an accessible gateway to a rich and active area of number theory. With an abundance of new topics and 50% more exe978-3-030-54945-9978-3-030-54946-6Series ISSN 0172-5939 Series E-ISSN 2191-6675

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