Abstract
In this chapter, we assume that the reader is conversant with the rudiments of Calculus. More precisely, we shall assume from the reader familiarity with convergent sequences and series, as well as with the notions of limits and derivatives of functions.
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Notes
- 1.
Jacques Hadamard , French mathematician of the nineteenth century.
- 2.
For a slightly different proof of such a result, see the problems of Section 10.9 of [8].
- 3.
Pafnuty Chebyshev , Russian mathematician of the nineteenth century.
- 4.
After Christian Goldbach , German mathematician of the eighteenth century.
- 5.
Ernesto Cesàro , Italian mathematician of the nineteenth century.
- 6.
As in previous chapters, we set I n = {1, 2, …, n}.
References
M. Aigner, G. Ziegler, Proofs from THE BOOK (Springer, Heidelberg, 2010)
G. Andrews, Number Theory (Dover, Mineola, 1994)
T. Apostol, Introduction to Analytic Number Theory (Springer, New York, 1976)
A. Caminha, An Excursion Through Elementary Mathematics I - Real Numbers and Functions (Springer, New York, 2017)
H.N. Lima, Limites e Funções Aritméticas (in Portuguese). Preprint
W. Rudin, Principles of Mathematical Analysis, 3rd edn. (McGraw-Hill, Inc., New York, 1976)
E. Stein, R. Shakarchi, Fourier Analysis: An Introduction (Princeton University Press, Princeton, 2003)
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Caminha Muniz Neto, A. (2018). Calculus and Number Theory. In: An Excursion through Elementary Mathematics, Volume III. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-77977-5_9
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