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Linear Mahler Measures and Double L-values of Modular Forms
Linear Mahler Measures Double L-values of Modular Forms Number Theory
2012/6/27
We consider the Mahler measure of the polynomial 1+x_1+x_2+x_3+x_4, which is the first case not yet evaluated explicitly. A conjecture due to F. Rodriguez-Villegas represents this Mahler measure as a ...
A characterization of ordinary modular eigenforms with CM
modular forms with complex multiplication Galois represenations Number Theory
2012/6/12
We show that a $p$-ordinary modular eigenform $f$ of weight $k\geq 2$, with $p$-adic Galois representation $\rho_f$ and $\mod{p^m}$ reductions $\rho_{f,m}$, and with complex multiplication(CM) is char...
Eichler Cohomology of Generalized Modular Forms of Real Weights
Eichler Cohomology Generalized Modular Forms Number Theory
2012/5/9
In this paper, we prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the...
Computing power series expansions of modular forms
power series expansions of modular forms Number Theory
2012/5/9
We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.
On the Petersson scalar product of arbitrary modular forms
Petersson scalar product arbitrary modular forms Number Theory
2012/4/18
We consider a natural extension of the Petersson scalar product to the entire space of modular forms of integral weight $k\ge 2$ for a finite index subgroup of the modular group. We show that Hecke op...
Ramanujan type congruences for modular forms of several variables
Congruences for modular forms Cusp forms Number Theory
2012/4/17
We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence o...
Abstract: Using lower bounds for linear forms in elliptic logarithms we determine the integral points of the modular curve associated to the normalizer of a non-split Cartan group of level 11. As an a...
Central characters for smooth irreducible modular representations of GL_2(Q_p)
Smooth representation admissible representation parabolic induction supersingular representation central character Schur’s lemma
2011/8/24
Abstract: We prove that every smooth irreducible F_p^alg-linear representation of GL_2(Q_p) admits a central character.
In a remarkable variety of contexts appears the modular data associated to finite groups. And yet, compared to the well-understood affine algebra modular data, the general properties of this finite g...