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Session

NT3: Number Theory Location: Audimax A600 Session Chair: Ozlem Imamoglu Session Chair: Anna-Maria Pippich

Presentation 1

Symplectic Kloosterman sums Árpád Tóth HUN-REN Alfréd Rényi Institute of Mathematics, Hungary The exponential sum \(\sum exp(2 \pi i tr(AX+X^{-1])/n) plays an important role in the theory of Siegel modular forms. The sum is oves symmetric invertible matrices modulo n. We give universal bounds that hold for all A. The crux of the matter is tha case when n is prime, when we also prove that are bounds are optimal by evaluating the sum directly when A is a scalar matrix.