Buser, PeterMakover, EranMuetzel, Bjoern2024-02-202024-02-202024-02-202023-12-1810.1007/s11856-023-2600-yhttps://infoscience.epfl.ch/handle/20.500.14299/204791WOS:001128356800002Given a hyperelliptic hyperbolic surface S of genus g >= 2, we find bounds on the lengths of homologically independent loops on S. As a consequence, we show that for any lambda is an element of (0, 1) there exists a constant N(lambda) such that every such surface has at least [lambda center dot 2/3 g] homologically independent loops of length at most N(lambda), extending the result in [Mu] and [BPS]. This allows us to extend the constant upper bound obtained in [Mu] on the minimal length of non-zero period lattice vectors of hyperelliptic Riemann surfaces to almost 2/3 g linearly independent vectors.Physical Sciencestext::journal::journal article::research article