Goldbach partitions and norms of cusp forms
An integral formula for the Goldbach partitions requires uniform convergence of a complex exponential sum. The dependence of the coefficients of the series is found to be bounded by that of cusp forms. Norms may be defined for these forms on a fundamental domain of a modular group. The relation wit...
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| Format: | Article |
| Jezik: | English |
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Publishing House of the Romanian Academy
2019-09-01
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| Serija: | Journal of Numerical Analysis and Approximation Theory |
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| Online dostop: | https://ictp.acad.ro/jnaat/journal/article/view/1152 |
| Izvleček: | An integral formula for the Goldbach partitions requires uniform convergence of a complex exponential sum. The dependence of the coefficients of the series is found to be bounded by that of cusp forms. Norms may be defined for these forms on a fundamental domain of a modular group. The relation with the integral formula is found to be sufficient to establish the consistency of the interchange of the integral and the sum, which must remain valid as the even integer $N$ tends to infinity.
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| ISSN: | 2457-6794 2501-059X |