On the Convergence of a Two-Dimensional Trigonometric Sum

✍ Scribed by Wolfgang Müller

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 133 KB
• Volume: 205
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5215

✦ Synopsis

By numerical experiments they were led to conjecture

The first published solution by J. Boersma and P. J. DeDoelder 1 confirms the first conjecture and disproves the second one numerically. Their proof has been criticized by several authors, since it ignores all w x questions of convergence. In 2 , D. Borwein and J. M. Borwein proved convergence in the Abel᎐Poisson sense. Concerning pointwise convergence they wrote: ''The problem of determining whether or not the series Ž . Ž . for S ¨or C ¨actually converge involves deep number theoretic quesw x tions which we cannot answer.'' Later, N. Ortner and P. Wagner 6 gave a 500