One special class of modular forms and group representations

It was shown in [14] and [15] that the con- ditioning of natural random Littelmann paths to stay in their corresponding Weyl chamber is controlled by central measures on this type

The Generalized Riemann Hypothesis (GRH) for L-function of modular forms states that all the non-trivial zeroes of these L-functions lie on the critical line Re s = 1 2.. Moreover,

We show that the p-adic eigenvariety constructed by Andreatta- Iovita-Pilloni, parameterizing cuspidal Hilbert modular eigenforms defined over a totally real field F , is smooth

The main objective, however, is to extend the representation ρ g to a 2-dimensional Galois representation with coefficients in the weight 1 Hecke algebra and to show, in most

For example, if G is any of the three groups A 4 , S 4 , A 5 , by using results on the existence or non-existence of generic or parametric polynomials/extensions with

As in the previous proof, for p > 2 by [Edixhoven 1992, Theorem 4.5], together with the remark at the end of the introduction to that article, the existence of a weight 1 form

Finally, in Chapter 4, we will prove that a partial weight one Hilbert modular form, with parallel weight one for the places above a prime p, has associated modulo $

the homology of the quotient spae in many ases of non-trivial lass group2. A ompletely dierent method to obtain