Let D be a negative discriminant, and let Θ(D) be the complex vector space generated by the binary theta series θf attached to the positive definite binary quadratic forms f(x, y) = ax + bxy + cy whose discriminant D(f) = b − 4ac equals D/t, for some integer t. It is a well-known classical fact that Θ(D) is a subspace of the space M1(|D|, ψD) of modular forms of weight 1, level |D| and Nebentyp...

We prove an automorphic analogue of Deligne's conjecture for symmetric fourth L-functions Hilbert modular forms. extend the result Morimoto [41] based on generalization and refinement results Grobner Lin [18] to cohomological irreducible essentially conjugate self-dual cuspidal representations GL2 GL3 over CM-fields.

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. As applications, we compute Shimura curve parametrizations of elliptic curves over a totally real field, including the image of CM points, and equations for Shimura curves.

Let k 2 Z and let SL 2 (Z) denote the special linear group SL 2 (Z) = a b c d : a; b; c; d 2 Z and ad bc = 1 : A modular form of weight k is an analytic function f de…ned on the complex upper half plane H = fz 2 C : Im(z) > 0g that transforms under the action of SL 2 (Z) according to the relation [1] f az + b cz + d = (cz + d) k f (z) for all a b c d 2 SL 2 (Z)

Abstract In this paper, we investigate the algebraic nature of value a higher Green function on an orthogonal Shimura variety at single CM point. This is motivated by conjecture Gross and Zagier in setting functions product two modular curves. process, will study analogue harmonic Maass forms Hilbert forms, obtain results concerning arithmetic their holomorphic part Fourier coefficients. As con...

Previous works have shown that certain weight 2 newforms are p-adic limits of weakly holomorphic modular forms under repeated application the U-operator. The proofs these theorems originally relied on theory harmonic Maass forms. Ahlgren and Samart obtained strengthened versions results using Here, we use such techniques to express all CM which eta quotients as limits. In particular, show deriv...