On the vanishing of the coefficients of CM eta quotients. (English) Zbl 07781898
Infinite multiplications with their convergence conditions and their applications occupy an important place in partition theory, especially in analytic number theory and complex analysis. The Dedekind eta function also is an important member of this infinite multiplication family. In particular, modular forms are among the most important elements of theta functions, elliptic functions and elliptic curves. This article is organized as follows. the authors review the notion of complex multiplication involving the Fourier coefficients, which is derived from Serre’s studies, newforms and their fundamentals, as well the complex multiplication of eta quotients given by tables in terms of generalized theta functions. The authors provide generalizations of the results on the cases of weight 1 in terms of binary quadratic forms. They also give many results and examples with related tables on the above content.
Reviewer: Yilmaz Simsek (Antalya)
MSC:
| 11F11 | Holomorphic modular forms of integral weight |
| 11F20 | Dedekind eta function, Dedekind sums |
| 11F30 | Fourier coefficients of automorphic forms |
References:
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