Petersson inner product

In mathematics the Petersson inner product is an inner product defined on the space of entire modular forms. It was introduced by the German mathematician Hans Petersson. In mathematics the Petersson inner product is an inner product defined on the space of entire modular forms. It was introduced by the German mathematician Hans Petersson. Let M k {displaystyle mathbb {M} _{k}} be the space of entire modular forms of weight k {displaystyle k} and S k {displaystyle mathbb {S} _{k}} the space of cusp forms. The mapping ⟨ ⋅ , ⋅ ⟩ : M k × S k → C {displaystyle langle cdot ,cdot angle :mathbb {M} _{k} imes mathbb {S} _{k} ightarrow mathbb {C} } ,