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ON SPRINDŽUK’S CLASSIFICATION OF
$p$-ADIC NUMBERS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 111 / Issue 2 / October 2021
- Published online by Cambridge University Press:
- 12 December 2019, pp. 221-231
- Print publication:
- October 2021
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We carry Sprindžuk’s classification of the complex numbers to the field
$\mathbb{Q}_{p}$ of 
$p$-adic numbers. We establish several estimates for the 
$p$-adic distance between 
$p$-adic roots of integer polynomials, which we apply to show that almost all 
$p$-adic numbers, with respect to the Haar measure, are 
$p$-adic 
$\tilde{S}$-numbers of order 1.
ON THE DISTANCE BETWEEN ROOTS OF INTEGER POLYNOMIALS
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 47 / Issue 3 / October 2004
- Published online by Cambridge University Press:
- 09 November 2004, pp. 553-556
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