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Fast evaluation of some p-adic transcendental functions

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Abstract

We design algorithms for computing values of many p-adic elementary and special functions, including logarithms, exponentials, polylogarithms, and hypergeometric functions. All our algorithms feature a quasi-linearccomplexity with respect to the target precision and most of them are based on an adaptation to the p-adic setting of the binary splitting and bit-burst strategies.
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hal-03263044 , version 1 (16-06-2021)

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Xavier Caruso, Marc Mezzarobba, Nobuki Takayama, Tristan Vaccon. Fast evaluation of some p-adic transcendental functions. 2021. ⟨hal-03263044⟩
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