Arithmetic Tales pp 297-353

# Exponential Sums

• Olivier Bordellès
Part of the Universitext book series (UTX)

## Abstract

As can be seen in the Dirichlet divisor problem, most of the great problems in multiplicative number theory require non-trivial estimates of exponential sums. In the early 1920s and 1930s, three different schools of thought investigated this problem. Following the lines of van der Corput, we provide the first criteria based upon the second and third derivatives of the studied function, and we apply them to the Dirichlet divisor problem. Many questions are also developed, such as the exponent pairs, the Vinogradov method, the Vaughan identity and the discrete Hardy–Littlewood method. This chapter could be considered as an analytic equivalent to Chap. .

## Keywords

Divisor Problem Large Sieve Diophantine Inequality Convolution Identity Exponent Pair
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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