Modular Forms of Varying Weight. II.
Modular forms of varying weights.
Modular parametrizations of certain elliptic curves
Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre differential operator. In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over ℚ, and as a consequence we generalize and explain some of their findings.
Modular symmetry and fractional charges in supersymmetric Yang-Mills and the quantum Hall effect.
Modulformen auf ... (N) mit rationalen Perioden.
Multiplier systems
Nearly ordinary deformations of irreducible residual representations
New examples of modular rigid Calabi-Yau threefolds.
The aim of this article is to present five new examples of modular rigid Calabi-Yau threefolds by giving explicit correspondences to newforms of weight 4 and levels 10, 17, 21 and 73.
New results on Ramanujan's function
Newforms of half-integral weight.
No -torsion on elliptic curves over cubic number fields
We complete our previous determination of the torsion primes of elliptic curves over cubic number fields, by showing that is not one of those.
Nonanalytic automorphic integrals on the Hecke groups
1. Introduction. Since its genesis over a century ago in work of Jacobi, Riemann, Poincar ́e and Klein [Ja29, Ri53, Le64], the theory of automorphic forms has burgeoned from a branch of analytic number theory into an industry all its own. Natural extensions of the theory are to integrals [Ei57, Kn94a, KS96, Sh94], thereby encompassing Hurwitz’s prototype, the analytic weight 2 Eisenstein series [Hu81], and to nonanalytic forms [He59, Ma64, Sel56, ER74, Fr85]. A generalization in both directions...
Nonvanishing theorems for L-functions of modular forms and their derivatives.
Note sur la sommation de la série de Lambert
Notes on the method of Frobenian functions with applications to Fourier coefficients of modular forms
Notiz über Modulargleichungen bei zusammengesetztem Transformationsgrad
Notiz zur Theorie der Modulfunctionen
Odd values of the Ramanujan -function
On a short spectral sum involving inner products of a holomorphic cusp form and Maass forms
On Automorphic Forms on the Unitary Symplectic Group Sp (n) and SL2 (R).