On real log canonical thresholds

Understand

We introduce real log canonical threshold and real jumping numbers for real algebraic functions.

• A real jumping number is a root of the $b$-function up to a sign if its difference with the minimal one is less than 1.
• The real log canonical threshold, which is the minimal real jumping number, coincides up to a sign with the maximal pole of the distribution defined by the complex power of the absolute value of the function.
• However, this number may be greater than 1 if the codimension of the real zero locus of the function is greater than 1.