On ordinary ...-adic representations associated to modular forms.
On -adic -functions of over totally real fields
Let be the Rankin product -function for two Hilbert cusp forms and . This -function is in fact the standard -function of an automorphic representation of the algebraic group defined over a totally real field. Under the ordinarity assumption at a given prime for and , we shall construct a -adic analytic function of several variables which interpolates the algebraic part of for critical integers , regarding all the ingredients , and as variables.
On singular moduli.
On sums of three squares
We address the question of when an integer in a totally real number field can be written as the sum of three squared integers from the field and more generally whether it can be represented by a positive definite integral ternary quadratic form over the field. In recent work with Piatetski-Shapiro and Sarnak we have shown that every sufficiently large totally positive square free integer is globally integrally represented if and only if it is so locally at all places, thus essentially resolving...
On symmetric and unsymmetric theta functions over a real quadratic field
On the anticyclotomic main conjecture for CM fields.
On the arithmetic of Siegel-Hilbert cuspforms: Petersson inner products and Fourier coefficients.
On the classification of Hilbert Modular threefolds.
On the critical values of certain Dirichlet series and the periods of automorphic forms.
On the Eisenstein series of Hilbert modular groups.
On the Geometry of a Siegel Modular Threefold.
On the graded rings of modular forms
On the Kodaira dimensions of Hilbert modular varieties.
On the Kuznetsov-Bruggeman Formula for a Hilbert Modular Surface Having One Cusp.
On the Kuznetsov-Bruggemann formula for a Hilbert modular surface having one cusp (Addendum).
On the meromorphic continuation of degree two -functions.
On the Resolution of Cusp Singularities and the Shintani Decomposition in Totally Real Cubic Number Fields.
On the Second L-Functions Attached to Hilbert Modular Forms.
On the spaces of Eisenstein series of Hilbert modular groups.
On the Theta Constant of Genus 8 and Hilbert Modular Groups over Certain Cyclic Biquadratic Fields.