Connexion de Gauss-Manin associ\'ee \`a la d\'eformationverselle de la   singularit\'e et z\'erosde l'int\'egrale hyperelliptique
  One studies the system of differential equations satisfied by the hyperelliptic integral associated to a vanishing cycle defined for the versal deformation of the $A-\mu$ singularity. As an application, the estimates on the multiplicity of zeros of the hyperelliptic integral are given as a linear function of the degree of present polynomials. 
Susumu Tanabe