Determinantal Formula for the Cuspidal Class Number of the Modular CurveX1(m)

Hazama, Fumio

doi:10.1006/jnth.1997.2210

Cited by 11 publications

(22 citation statements)

References 4 publications

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“…On the other hand, the matrix M( p; 2) is equal to the matrix M p in [3]. Hence our theorem can be considered to be a natural generalization of the results in those articles.…”

Section: Generalization Of the Demjanenko Matrixmentioning

confidence: 75%

“…Our proof is based on the method employed in [2,3] of which the former treated the case n=1 and the latter the case n=2. First we consider the case n is odd.…”

Section: Generalization Of the Demjanenko Matrixmentioning

confidence: 99%

“…Recently in [3], the determinant of a certain integer matrix, introduced by Silverman in [5], is shown to compute the cuspidal class number of the modular curve X 1 (m). Since the class numbers in both cases are essentially expressed as the values at s=0 (resp.…”

Section: Introductionmentioning

confidence: 99%

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Determinantal Formula for the Special Values of the Dedekind Zeta Function of the Cyclotomic Field

Hazama

1999

Journal of Number Theory

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“…On the other hand, the matrix M( p; 2) is equal to the matrix M p in [3]. Hence our theorem can be considered to be a natural generalization of the results in those articles.…”

Section: Generalization Of the Demjanenko Matrixmentioning

confidence: 75%

“…Our proof is based on the method employed in [2,3] of which the former treated the case n=1 and the latter the case n=2. First we consider the case n is odd.…”

Section: Generalization Of the Demjanenko Matrixmentioning

confidence: 99%

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Determinantal Formula for the Special Values of the Dedekind Zeta Function of the Cyclotomic Field

Hazama

1999

Journal of Number Theory

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“…The proof of the first statement is a straightforward computation. Then the second statement follows immediately from (6) …”

Section: (5)mentioning

confidence: 91%

Modular units and cuspidal divisor class groups of X1(N)

Yang

2009

Journal of Algebra

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In this article, we consider the group F ∞ 1 (N) of modular units on X 1 (N) that have divisors supported on the cusps lying over ∞ of X 0 (N), called the ∞-cusps. For each positive integer N, we will give an explicit basis for the group F ∞ 1 (N). This enables us to compute the group structure of the rational torsion subgroup C ∞ 1 (N) of the Jacobian J 1 (N) of X 1 (N) generated by the differences of the ∞-cusps. In addition, based on our numerical computation, we make a conjecture on the structure of the p-primary part of C ∞ 1 (p n ) for a regular prime p.

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“…Hazama's recent paper [13] has come into our attention, which calculates the special values of the Dedekind zeta-functions of prime cyclotomic fields. The essential ingredient is the function f n (a), which is nothing but…”

Section: Proof Of Theoremsmentioning

confidence: 99%

On a generalization of the Maillet determinant II

Kanemitsu¹,

Kuzumaki²

2001

Acta Arith.

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Dedicated to Professor Katsuya Miyake on his sixtieth birthday 1. Introduction. In the previous paper [16] (referred to as Part I hereafter) we have rendered it visible that the two intimately connected problems of number theory, Maillet determinants and Chowla's problem, were dealt with in complete separation, save for Girstmair [11], where this interaction was duly noticed and proved to be crucial.

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Determinantal Formula for the Cuspidal Class Number of the Modular CurveX1(m)

Cited by 11 publications

References 4 publications

Determinantal Formula for the Special Values of the Dedekind Zeta Function of the Cyclotomic Field

Determinantal Formula for the Special Values of the Dedekind Zeta Function of the Cyclotomic Field

Modular units and cuspidal divisor class groups of X1(N)

On a generalization of the Maillet determinant II

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