On automorphic forms on algebraic groups: Arithmetic invariants and automorphic L-functions

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Several invariants are attached to automorphic forms on algebraic groups. These invariants and relationships between them are very useful for studying the internal structure of automorphic forms. In this research, we investigated relationships between these invariants for automorphic forms of special kind called Aarkawa liftings. Using this result, we proposed certain conjectures on relations between invariants attached to automorphic forms on certain groups. We showed that automorphic forms called Borcherds products have strong symmetries (the multiplicative symmetries). We also studied the Borcherds products in detail in the genus two Siegel modular case. In particular, we obtained several results about the weights and characters of Borcherds products.