Immunoglobulin A only weakly. IgA exists in two isotypes, IgA1 and IgA2. They are both heavily glycosylated proteins. While IgA1 predominates in serum (~80%), IgA2 percentages are higher in secretions than in serum (~35% in secretions); the ratio of IgA1 and IgA2 secreting cells varies in the different lymphoid tissues of the human body: Both IgA1 and IgA2 have been found in external secretions like colostrum, maternal milk, tears and saliva, where IgA2 is more prominent than in the blood. Polysaccharide antigens tend to induce more IgA2 than protein antigens. Both IgA1 and IgA2 can be in membrane-bound form. ("see B-cell receptor")
Harmonic Maass form combinatorial, arithmetic, or geometric generating functions. Regularized theta lifts of harmonic Maass forms can be used to construct Arakelov Green functions for special divisors on orthogonal Shimura varieties. A complex-valued smooth function on the upper half-plane is called a weak Maass form of integral weight (for the group ) if it satisfies the following three conditions: If is a weak Maass form with eigenvalue 0 under formula_4, that is, if formula_5, then is called a harmonic weak Maass form, or briefly a harmonic Maass form. Every harmonic Maass form of weight has a Fourier expansion of the form where ,