Proceedings of the Glasgow Mathematical Association · 1964 · 48 citations · 2 references
Natural SciencesMathematicsPhysicsCondensed Matter PhysicsNuclear PhysicsNumber TheoryAnalytic Number TheoryModular FormsPositive Definite FunctionsPositive Definite Quadratic FormsRiemann Zeta FunctionSingularity Structure
Let h (m, n) = α m 2 + 2δ mn + β n 2 be a positive definite quadratic form with determinant αβ–δ 2 = 1. It may be put in the shape with y > 0. We write (for s > 1) The function Z n (s) may be analytically continued over the whole s -plane. Its only singularity is a simple pole with residue π at s = 1.
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