Galois representations
Galois representations, embedding problems and modular forms.
To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations...
Galois representations, Hecke operators, and the cohomology of with twisted coefficients.
Galois representations into GL2(Zp[[X]]) attached to ordinary cusp forms.
Galois representations modulo p and cohomology of Hilbert modular varieties
Galois representations of dihedral type over ℚₚ
Galois representations of octahedral type and 2-coverings of elliptic curves.
Gaps Between Consecutive Zeros of the Riemann Zeta-Function on the Critical Line.
Gauss Sums and Elliptic Functions: II. The Quartic Sum.
Gauss–Manin connections for -adic families of nearly overconvergent modular forms
We interpolate the Gauss–Manin connection in -adic families of nearly overconvergent modular forms. This gives a family of Maass–Shimura type differential operators from the space of nearly overconvergent modular forms of type to the space of nearly overconvergent modular forms of type with -adic weight shifted by . Our construction is purely geometric, using Andreatta–Iovita–Stevens and Pilloni’s geometric construction of eigencurves, and should thus generalize to higher rank groups.
Gauss's ₂F₁ hypergeometric function and the congruent number elliptic curve
Genera of arithmetic Fuchsian groups
Genera of congruence subgroups in Q-quaternion algebras.
Generalization of the symplectic modular group
Generalizations of Dedekind sums and their reciprocity laws
Generalized continued fractions and orbits under the action of Hecke triangle groups
Generalized Dedekind sums.
Generalized Dedekind sums, correlation of L-series, and the Galois module of cot(π/N)cot(mπ/N)
Generalized divisor problem for new forms of higher level
Suppose that is a primitive Hecke eigenform or a Mass cusp form for with normalized eigenvalues and let be a real number. We consider the sum and show that for every and . The same problem was considered for the case , that is for the full modular group in Lü (2012) and Kanemitsu et al. (2002). We consider the problem in a more general setting and obtain bounds which are better than those obtained by the classical result of Landau (1915) for . Since the result is valid for arbitrary...
Generalized Eisenstein series and modified Dedekind sums.