The a-number of an algebraic curve \({\mathcal {X}}\) is the dimension of the space of exact holomorphic differentials on \({\mathcal {X}}\). In this paper, we give a formula for the a-number of family of hyperelliptic curves defined by the equations \(y^2=x^{m}+1\) and \(y^2=x^{m}+x\) for infinitely many values of m.

中文翻译：

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某超椭圆曲线的a数

代数曲线\({\mathcal {X}}\)的a数是 \({ \ mathcal {X}}\)上的精确全纯微分空间的维数。在本文中，我们给出了由方程\(y^2=x^{m}+1\)和\(y^2=x^{m}+ x\)用于无限多个m值。