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Sander Zwegers
Sander Pieter Zwegers (born April 16, 1975) is a Dutch mathematician who made a connection between Maass forms and Srinivasa Ramanujan's mock theta functions in 2002. He was born in Oosterhout. After a period at the Max-Planck Institute in Bonn, he became an assistant professor at the University College Dublin in 2008. Since 2011, he has been is professor of number theory at the University of Cologne. Research In 1976, the American mathematician George Andrews found what is nowadays known as the "Lost Notebook" of Ramanujan. It contains many remarkable results, including the mysterious mock theta functions. This notebook contains what many specialists regard as Ramanujan’s deepest work. It was Sander Zwegers who, as a PdD student, had groundbreaking ideas how to fit the mock theta functions into a broader context. His 2002 PhD thesis has led to numerous publications and international conferences.Peter LynchTimely reminder of a mathematical genius The Irish Times, Dec 6, 2012. Z ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maass Form
In mathematics, Maass forms or Maass wave forms are studied in the theory of automorphic forms. Maass forms are complex-valued smooth functions of the upper half plane, which transform in a similar way under the operation of a discrete subgroup \Gamma of \mathrm_(\R) as modular forms. They are Eigenforms of the hyperbolic Laplace Operator \Delta defined on \mathbb and satisfy certain growth conditions at the cusps of a fundamental domain of \Gamma. In contrast to the modular forms the Maass forms need not be holomorphic. They were studied first by Hans Maass in 1949. General remarks The group : G := \mathrm_(\R) = \left\ operates on the upper half plane :\mathbb = \ by fractional linear transformations: :\begin a & b \\ c & d \\ \end \cdot z := \frac. It can be extended to an operation on \mathbb \cup \ \cup \mathbb by defining: :\begin a & b \\ c & d \\ \end\cdot z :=\begin \frac & \text cz+d \neq 0, \\ \infty & \text cz+d=0,\end :\begin a & b \\ c & d \\ \end \cdot \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |