2000 Fiscal Year Final Research Report Summary
Construction of newform theory for modular forms of half-integral weight
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants |
|Research Institution||Nara Women's University |
UEDA Masaru Nara Women's University, Faculty of Science Professor, 理学部, 教授 (80193811)
|Project Period (FY)
1998 – 2000
|Keywords||modular forms / half-integral weight / trace formula / twisting operator|
The purpose of our research is to construct a theory of newforms of half-integral weight. We investigated this subject from April 1998 to March 2001. And we have the following two results.
First, we made a refinement of the previous work. We had already got a theory of newforms for Kohnen spaces. However, in some cases, non-pure newforms occur in the space of newforms of Kohnen spaces. We succeeded in removing such non-pure newforms under a certain week condition. The main tool of this is to use twisting operators of quartic Dirichlet characters.
Next, we investigated cusp forms of half-integral weight and of level divisible by 32. In such cases, there is not a theory of newforms yet.
We introduced completely different twisting operators from the previous one.By using these operators, we could make a theory of newforms in several cases.
Moreover, we collaborated with Professor A.Murase for investigation of trace relations. Trace relations are most important for contruction of theory of newforms.But, we do not understand why trace relations exist yet.
We made an numerical experiment on this subject. As a result, we consider that Shintani lift seems to play an important role. Now we are investigating this observation.
Research Products (2 results)