For a knot in the 3-sphere, the upsilon invariant is a piecewise linear function defined on the interval [0,2]. It is known that for an L-space knot, the upsilon invariant is determined only by the Alexander polynomial. We exhibit infinitely many pairs of hyperbolic L-space knots such that two knots of each pair have distinct Alexander polynomials, so they are not concordant, but share the same Upsilon invariant. Conversely, we examine the restorability of the Alexander polynomial of an L-space knot from the upsilon invariant through the Legendre-Fenchel transformation.

The author has been supported by JSPS KAKENHI Grant Number 20K03587.