Volovich states in P-adic Analysis and Mathematical Physics (pages 54, 55) that the following function:

$$\lambda_p(a) = \begin{cases}1 & v_p(a) \mbox{ is even} \\ \Bigl(\frac{a_0}p \Bigr) & v_p(a) \mbox{ is odd and } p \equiv 1 \mod 4 \\ i \Bigl(\frac{a_0}p \Bigr) & v_p(a) \mbox{ is odd and } p \equiv 3 \mod 4 \end{cases}$$

is of great importance but refuses to name it implicitly. $\Bigl(\frac ab\Bigr)$ denotes the Legendre symbol and $v_p$ is the $p$-adic valuation. What is its name?

Here $a = p^n(a_0 + a_1p + a_2p^2+ \ldots)$ is a $p$-adic number.

  • $\begingroup$ Is $a$ a number or a sequence? Because you have used $a_0$ in the definition. $\endgroup$ – Mark Fischler Sep 21 '16 at 14:36
  • $\begingroup$ @MarkFischler it's a $p$-adic number. $\endgroup$ – Santiago Sep 21 '16 at 14:59
  • $\begingroup$ Who is Volovich ? Could you give a reference ? $\endgroup$ – Jean Marie Sep 21 '16 at 16:09
  • $\begingroup$ @JeanMarie I've added a hyperlink. $\endgroup$ – Santiago Sep 22 '16 at 10:37

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