2001 Fiscal Year Final Research Report Summary
The special values of the L function associated with automorphic forms
| Project/Area Number |
12640049
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Ritsumeikan University |
|---|
Principal Investigator |
ISHII Hidenori Ritsumeikan Univ., Fac. Science and Engineering, Professor, 理工学部, 教授 (60159671)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NARUKI Isao Ritsumeikan Univ., Fac. Science and Engineering, Professor, 理工学部, 教授 (90027376)
NAKAJIMA Kazufumi Ritsumeikan Univ., Fac. Science and Engineering, Professor, 理工学部, 教授 (10025489)
ARAI Masaharu Ritsumeikan Univ., Fac. Science and Engineering, Professor, 理工学部, 教授 (20066715)
KAGAWA Takaaki Ritsumeikan Univ., Fac. Science and Engineering, Associate Professor, 理工学部, 助教授 (90298175)
YAMADA Osanobu Ritsumeikan Univ., Fac. Science and Engineering, Professor, 理工学部, 教授 (70066744)
|
|---|
| Project Period (FY) |
2000 – 2001
|
| Keywords | Automorphic forms / L-function / Hilbert cusp forms |
|---|
| Research Abstract |
(1) In this research, we improved the previous results which concern between cups forms. To be precise, we prove the existence of primitive cusp form of arbitrary weight which is congruent to the cusp form of weight one which associated with ray class character of quadratic number field. This result is a generalization of previous theorem which is proved m 1981. Key of the proof is a study of the generalized Bernoulli numbers. Some integrality properties which concern with the Bernoulli numbers are newly proved. The primitivity is a result of previous research.
(2) Calculations of the eigenvalues of the Hecke operators in the space of Hilbert cusp forms over totally real number fields is died for sufficiently general fields. Therefore, the rational structure is studied. Numerical examples of the Hecke fields and the special values of twisted adjoin L functions are newly added which supports the conjecture of Doi-Hida-Ishii in invent. math. 1998
(3) Elliptic curves defined over some quadratic number fields with everywhere good reduction or small conductor are determined by T. Kagawa.
(4) O. Yamada give some results about the essential self-adointness of the Dirac operators.
|
