Abstract
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.
Publisher
Academia Romana Filiala Cluj
Reference14 articles.
1. G. H. Hardy and J. E. Littlewood, Some Problems of ‘Partitio Numerorum’ (V): A Further Contribution ot the Study of Goldbach’s Problem, Proc. London Math. Soc. (2)22(1924) 46-56. https://doi.org/10.1112/plms/s2-22.1.46
2. S. Davis, On the Existence of a Non-Zero Lower Bound for the Number of Goldbach Partitions of an Even Integer, Int. J. Math. Mathemat. Sci. (2004) 789-798. https://doi.org/10.1155/s0161171204307295
3. S. Davis, A Recursion Relation for the Number of Goldbach Partitions of an Even Integer, RFSC-04-07.
4. H. Weyl, Uber die Gleichverteilung von Zahlen mod Eins, Math. Ann. 77 (1916) 313-352. https://doi.org/10.1007/bf01475864
5. I. M. Vinogradov, Representation of an Odd Number of a Sum of Three Primes, Doklady Akad. Sciences USSR 15 (1937) 191-294.