The first 128 digits of an autoconvolution inequality
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910015203311616 |
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| author | Rechnitzer, Andrew |
| author_facet | Rechnitzer, Andrew |
| contents | Using rigorous high-precision floating point arithmetic we compute very tight rigorous bounds on the auto-convolution constant \[
ν_2^2 = \inf_f \|f \ast f\|_2^2 = \inf_f \int_{-1}^1 (f \ast f)^2 \] where the infimum is taken over all unit mass functions $f \in L^1(-1/2,1/2)$. This quantity arises in additive combinatorics, particularly in the study of Sidon sets. Our bounds give the first 128 digits of $ν_2^2$, and so substantially improve previous bounds on this quantity due to White, Green, and Martin & O'Bryant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07292 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The first 128 digits of an autoconvolution inequality Rechnitzer, Andrew Number Theory Combinatorics 05-08, 11B13, 42A05, 42A85 Using rigorous high-precision floating point arithmetic we compute very tight rigorous bounds on the auto-convolution constant \[ ν_2^2 = \inf_f \|f \ast f\|_2^2 = \inf_f \int_{-1}^1 (f \ast f)^2 \] where the infimum is taken over all unit mass functions $f \in L^1(-1/2,1/2)$. This quantity arises in additive combinatorics, particularly in the study of Sidon sets. Our bounds give the first 128 digits of $ν_2^2$, and so substantially improve previous bounds on this quantity due to White, Green, and Martin & O'Bryant. |
| title | The first 128 digits of an autoconvolution inequality |
| topic | Number Theory Combinatorics 05-08, 11B13, 42A05, 42A85 |
| url | https://arxiv.org/abs/2602.07292 |