Convolution and square in abelian groups III
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929202358386688 |
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| author | Benoist, Yves |
| author_facet | Benoist, Yves |
| contents | In the first paper we proved that on the cyclic groups of odd order d, there exist non zero functions whose convolution square f*f(2t) is proportional to their square f(t)^2 when the proportionality constant is an odd algebraic integer of norm d whose both real and imaginary part are square roots of integers. We show here that the function f can be chosen to be equal to the conjugate of its Fourier transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convolution and square in abelian groups III Benoist, Yves Number Theory In the first paper we proved that on the cyclic groups of odd order d, there exist non zero functions whose convolution square f*f(2t) is proportional to their square f(t)^2 when the proportionality constant is an odd algebraic integer of norm d whose both real and imaginary part are square roots of integers. We show here that the function f can be chosen to be equal to the conjugate of its Fourier transform. |
| title | Convolution and square in abelian groups III |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.03716 |