On congruence modules associated to -adic forms
On Cramér's theorem for general Euler products with functional equation.
On critical values of twisted Artin -functions
We give a simple proof that critical values of any Artin -function attached to a representation with character are stable under twisting by a totally even character , up to the -th power of the Gauss sum related to and an element in the field generated by the values of and over . This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.
On cubic symplectic metaplectic forms.
On cusp forms for co-finite subgroups of PSL(2, IR).
On Cusp Forms in Character Varieties.
On determination of GL₃ cusp forms
On differential operators attached to certain representations of classical groups.
On Dirchlet's series satisfying Riemann's functional equation.
On Dirichlet series and Hecke triangle groups of infinite volume
On Dirichlet Series and Petersson Products for Siegel Modular Forms
We prove that the Dirichlet series of Rankin–Selberg type associated with any pair of (not necessarily cuspidal) Siegel modular forms of degree and weight has meromorphic continuation to . Moreover, we show that the Petersson product of any pair of square–integrable modular forms of weight may be expressed in terms of the residue at of the associated Dirichlet series.
On Dirichlet series associated with cubic Gauss sums.
On distinguished representations.
On effective determination of symmetric-square lifts
Let F be the symmetric-square lift with Laplace eigenvalue λ F (Δ) = 1+4µ2. Suppose that |µ| ≤ Λ. We show that F is uniquely determined by the central values of Rankin-Selberg L-functions L(s, F ⋇ h), where h runs over the set of holomorphic Hecke eigen cusp forms of weight κ ≡ 0 (mod 4) with κ≍ϱ+ɛ, t9 = max {4(1+4θ)/(1−18θ), 8(2−9θ)/3(1−18θ)} for any 0 ≤ θ < 1/18 and any ∈ > 0. Here θ is the exponent towards the Ramanujan conjecture for GL2 Maass forms.
On Eisenstein series with characters and Dedekind sums
On Eisenstein series with characters and the values of Dirichlet L-functions
On elliptic Galois representations and genus-zero modular units
Given an odd prime and a representation of the absolute Galois group of a number field onto with cyclotomic determinant, the moduli space of elliptic curves defined over with -torsion giving rise to consists of two twists of the modular curve . We make here explicit the only genus-zero cases and , which are also the only symmetric cases: for or , respectively. This is done by studying the corresponding twisted Galois actions on the function field of the curve, for which...
On Elliptic Units and Class Number of a Certain Non-Galois Number Field.
On embedding numbers into quaternion orders.
On endo-lifting