Eigenfunctions of the Fourier Transform with specified zeros
| Autor: | Douglas P. Hardin, Ahram S. Feigenbaum, Peter J. Grabner |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Uncertainty principle Laplace transform Mathematics - Number Theory General Mathematics 010102 general mathematics Context (language use) Metric Geometry (math.MG) Function (mathematics) Eigenfunction 01 natural sciences symbols.namesake Fourier transform Mathematics - Metric Geometry Mathematics - Classical Analysis and ODEs 0103 physical sciences symbols Classical Analysis and ODEs (math.CA) FOS: Mathematics 010307 mathematical physics Number Theory (math.NT) 0101 mathematics Leech lattice Fourier series Mathematics |
| Popis: | Eigenfunctions of the Fourier transform with prescribed zeros played a major role in the proof that theE8and the Leech lattice give the best sphere packings in respective dimensions 8 and 24 by Cohn, Kumar, Miller, Radchenko and Viazovska. The functions used for a linear programming argument were constructed as Laplace transforms of certain modular and quasimodular forms. Similar constructions were used by Cohn and Gonçalves to find a function satisfying an optimal uncertainty principle in dimension 12. This paper gives a unified view on these constructions and develops the machinery to find the underlying forms in all dimensions divisible by 4. Furthermore, the positivity of the Fourier coefficients of the quasimodular forms occurring in this context is discussed. |
| Databáze: | OpenAIRE |
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