Let $ X $ be a smooth geometrically connected projective curve over the field of fractions of
a discrete valuation ring $ R $, and $\mathfrak {m} $ a modulus on $ X $, given by a closed …

We define and study the space of mixed modular symbols for a given finite index subgroup
$\Gamma $ of $\operatorname {SL} _2 (\mathbf {Z}) $. This is an extension of the usual …

For a positive integer N, let C (N) be the subgroup of J 0 (N) generated by the equivalence
classes of cuspidal divisors of degree 0 and C (N)(Q):= C (N)∩ J 0 (N)(Q) be its Q-rational …

We consider the generalized Jacobian J~ of the modular curve X 0⁢(N) of level N with
respect to a reduced divisor consisting of all cusps. Supposing N is square free, we explicitly …

We consider the generalised Jacobian $ J_ {0}(N) _ {\mathbf {m}} $ of the modular curve $
X_ {0}(N) $ of level $ N $, with respect to the modulus $\mathbf {m} $ consisting of all cusps …

We consider the generalised Jacobian J0 (N) m of the modular curve X0 (N) of level N, with
respect to the modulus m consisting of all cusps on the modular curve. When N is odd, we …