In this article, we shall study, using elementary and combinatorial methods, the distribution of quadratic non-residues which are not primitive roots modulo p h or 2p h for an odd prime p and h ≥ 1 is an integer.
Using the relationship between Jacobi forms of half-integral weight and vector valued modular forms, we obtain the number of components which determine the given Jacobi form of index p, p 2 or pq, where p and q are odd primes.
In this paper, we determine all modular forms of weights 36 ≤ k ≤ 56, 4 | k, for the full modular group SL 2 (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 R 3 (resp. in R 4) for the cases k = 36,… (More)