Journal article
A FOURIER ANALYSIS APPROACH TO DISPROVE THE WEAK SHANKS CONJECTURE
Proceedings of the American Mathematical Society, v 154(6), pp 2479-2486
06 Mar 2026
Abstract
<p>We derive formulas for the Fourier coefficients of |f |(2), where f(z(1), z(2))= (1-z(1), z(2)/r ), (-alpha ),alpha > 0, in terms of hypergeometric functions. Using these formulas we provide additional counterexamples to the weak Shanks conjecture, which was recently disproven by Beneteau, Khavinson and Seco [Constr. Approx. 62 (2025), pp. 645-661]. The obtained formulas allow for (numerical) optimization over the parameters alpha and r.</p>
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Details
- Title
- A FOURIER ANALYSIS APPROACH TO DISPROVE THE WEAK SHANKS CONJECTURE
- Creators
- Jeffrey GeronimoHugo Woerdeman
- Publication Details
- Proceedings of the American Mathematical Society, v 154(6), pp 2479-2486
- Publisher
- American Mathematical Society
- Number of pages
- 8
- Grant note
- National Science Foundation: DMS 2348720
The second author was partially supported by National Science Foundation grant DMS 2348720.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001743635900001
- Other Identifier
- 991022171475504721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied