Harmonic weak Maass-modular grids in higher level cases
We extend Guerzhoy's Maass-modular grids on the full modular group SL₂(ℤ) to congruence subgroups Γ₀(N) and Γ₀⁺(p).
We extend Guerzhoy's Maass-modular grids on the full modular group SL₂(ℤ) to congruence subgroups Γ₀(N) and Γ₀⁺(p).
We give a geometric interpretation of an arithmetic rule to generate explicit formulas for the Fourier coefficients of elliptic modular forms and their associated Jacobi forms. We discuss applications of these formulas and derive as an example a criterion similar to Tunnel's criterion for a number to be a congruent number.
We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi- Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers. The construction is based on a group representation arising from the transformation formula of a set of theta series.