I was reading An Introduction to the Theory of Numbers by Hardy and Wright, and on pages 66 and 67, I encountered the notation, as following enter image description here enter image description here What does the $e( )$ and $e\{\}$ notation mean? Any help would be most appreciated! Thanks, BakedPotato66

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    $\begingroup$ The definition of the $e$ function is given in the first display of p. 66: $e(x) = \mathrm{e}^{2\pi \mathrm{i}x}$. $\endgroup$ Commented Jun 21 at 21:32

1 Answer 1


That first line basically defines $e(x)$, it's shorthand for writing

$$e(x) = e^{2 \pi i x}$$

in a way which saves having to insert the $2 \pi i$ factor every time.

$\{ - \}$ appears to just be "larger parentheses," as far as I can tell, and you can see that it's used that way later in the text. I don't know why the authors felt it was necessary on that second line.

  • $\begingroup$ Perhaps they used braces on the left side of that second line because there are already regular parentheses in that expression $\endgroup$ Commented Jun 21 at 21:48
  • $\begingroup$ Yes, but those parentheses are small! $\endgroup$ Commented Jun 21 at 21:49

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