CUSPIDAL CLASS NUMBER FORMULA 181 the group ring. In Section 3, we prove that all modular units on the ลฝ . modular curve X M can be written as products of the functions h and 0 rational numbers. In Section 4, we determine a necessary and sufficient condition under which a product of the functions h
Determinantal Formula for the Cuspidal Class Number of the Modular CurveX1(m)
โ Scribed by Fumio Hazama
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 313 KB
- Volume
- 68
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
โฆ Synopsis
An integer matrix whose determinant computes the cuspidal class number of the modular curve X 1 (m) is obtained. When m is an odd prime, this will provide us with an upper bound of the class number.
๐ SIMILAR VOLUMES
## Abstract It has been long conjectured that the crossing number of __C~m~__โรโ__C~n~__ is (__m__โ2)__n__, for all __m__, __n__ such that __n__โโฅโ __m__โโฅโ 3. In this paper, it is shown that if __n__โโฅโ __m__(__m__โ+โ1) and __m__โโฅโ 3, then this conjecture holds. That is, the crossing number of __
For every integer m โฅ 3 and every integer c, let r m c be the least integer, if it exists, such that for every 2-coloring of the set 1 2 r m c there exists a monochromatic solution to the equation The values of r m c were previously known for all values of m and all nonnegative values of c. In this