Fe b 20 05 Modular representations on some Riemann - Roch spaces of modular curves X ( N )

Modular representations on some Riemann-Roch spaces of modular curves X(N)

We compute the PSL(2, N)-module structure of the Riemann-Roch space L(D), where D is an invariant non-special divisor on the modular curve X(N), with N ≥ 7 prime. This depends on a computation of the ramification module, which we give explicitly. These results hold for characteristic p if X(N) has good reduction mod p and p does not divide the order of PSL(2, N). We give as examples the cases N...

Fixed points for Banach and Kannan contractions in modular spaces with a graph

In this paper, we discuss the existence and uniqueness of xed points for Banach and Kannancontractions dened on modular spaces endowed with a graph. We do not impose the Δ2-conditionor the Fatou property on the modular spaces to give generalizations of some recent results. Thegiven results play as a modular version of metric xed point results.

0 D ec 2 00 2 REPRESENTATIONS OF FINITE GROUPS ON RIEMANN - ROCH SPACES

We study the action of a finite group on the Riemann-Roch space of certain divisors on a curve. If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X left stable by G then we show the natural representation of G on the Riemann-Roch space L(D) = LX (D) is a direct sum of irreducible representations of dimension ≤ d, where d is the size of the smalles...

Some functional inequalities in variable exponent spaces with a more generalization of uniform continuity condition

‎Some functional inequalities‎ ‎in variable exponent Lebesgue spaces are presented‎. ‎The bi-weighted modular inequality with variable exponent $p(.)$ for the Hardy operator restricted to non‎- ‎increasing function which is‎‎$$‎‎int_0^infty (frac{1}{x}int_0^x f(t)dt)^{p(x)}v(x)dxleq‎‎Cint_0^infty f(x)^{p(x)}u(x)dx‎,‎$$‎ ‎is studied‎. ‎We show that the exponent $p(.)$ for which these modular ine...

Some result on modular hyperconvex spaces