アルティン・ハッセの指数関数
Artin, E.; Hasse, H. (1928), “Die beiden Ergänzungssätze zum Reziprozitätsgesetz der ln-ten Potenzreste im Körper der ln-ten Einheitswurzeln”, Abhandlungen Hamburg 6: 146–162, JFM 54.0191.05
A course in p-adic analysis, by Alain M. Robert
Fesenko, Ivan B.; Vostokov, Sergei V. (2002), Local fields and their extensions, Translations of Mathematical Monographs, 121 (Second ed.), Providence, RI: American Mathematical Society, ISBN 978-0-8218-3259-2, MR1915966
We can use either formula for Ep(x) to prove that, unlike e, all of its coefficients are p-integral; in other words, the denominators of the coefficients of Ep(x) are not divisible by p. A first proof uses the definition of Ep(x) and Dwork's lemma, which says that a power series f(x) = 1 + ... with rational coefficients has p-integral coefficients if and only if f(x)/f(x) ≡ 1 mod pZp[[x]]. When f(x) = Ep(x), we have f(x)/f(x) = e, whose constant term is 1 and all higher coefficients are in pZp.