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Primitive Automorphic Forms

In: Mathematics Unlimited — 2001 and Beyond

Author

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  • Kyoji Saito

Abstract

There seems to be a marvellous interaction taking place between mathematical physics and mathematics in the area of geometry, demanding a greater contribution from non-commutative structures and higher cohomologies. It may require a revolutional extension of the concept of spaces in order to explain the dualities there. I am not the proper person to talk about the whole subject, but will restrict myself to that part of the topic where I have been involved from the view point of complex geometry, namely periods of integrals over vanishing cycles. In order to attack a big mathematical problem, there are two approaches: 1) to generalize the problem and to develop a new general framework and language within which the problem finds a natural place, or 2) to attempt to examine a cross-section of the problem and to give a precise solution of that part of the problem.

Suggested Citation

  • Kyoji Saito, 2001. "Primitive Automorphic Forms," Springer Books, in: Björn Engquist & Wilfried Schmid (ed.), Mathematics Unlimited — 2001 and Beyond, pages 1003-1018, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-56478-9_51
    DOI: 10.1007/978-3-642-56478-9_51
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