Plücker forms and the theta map

Mock Theta Functions, Ranks, and Maass Forms

Mock Theta Functions and Quantum Modular Forms

Ramanujan’s last letter to Hardy concerns the asymptotic properties of modular forms and his ‘mock theta functions’. For the mock theta function f (q), Ramanujan claims that as q approaches an even-order 2k root of unity, we have f (q)− (−1)(1− q)(1− q)(1− q) · · · (1− 2q+ 2q − · · ·)= O(1). We prove Ramanujan’s claim as a special case of a more general result. The implied constants in Ramanuja...

Modular forms which behave like theta series

In this paper, we determine all modular forms of weights 36 ≤ k ≤ 56, 4 | k, for the full modular group SL2(Z) which behave like theta series, i.e., which have in their Fourier expansions, the constant term 1 and all other Fourier coefficients are non–negative rational integers. In fact, we give convex regions in R3 (resp. in R4) for the cases k = 36, 40 and 44 (resp. for the cases k = 48, 52 a...

The e-Theta Hopes

The largest class of hyperstructures is the Hv-structures, introduced in 1990, which proved to have a lot of applications in mathematics and several applied sciences, as well. Hyperstructures are used in the Lie-Santilli theory focusing to the hypernumbers, called e-numbers. We present the appropriate e-hyperstuctures which are defined using any map, in the sense the derivative map, called thet...

On the Image of Code Polynomials under Theta Map

The theta map sends code polynomials into the ring of Siegel modular forms of even weights. Explicit description of the image is known for g ≤ 3 and the surjectivity of the theta map follows. Instead it is known that this map is not surjective for g ≥ 5. In this paper we discuss the possibility of an embedding between the associated projective varieties. We prove that this is not possible for g...