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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.03234 |
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| _version_ | 1866909985152172032 |
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| author | Berndt, Bruce C. Bhat, Raghavendra N. Meyer, Jeffrey L. Xie, Likun Zaharescu, Alexandru |
| author_facet | Berndt, Bruce C. Bhat, Raghavendra N. Meyer, Jeffrey L. Xie, Likun Zaharescu, Alexandru |
| contents | The sum $S(h,k):=\sum_{j=1}^{k-1}(-1)^{j+1+[hj/k]}$ appears in the modular transformation formulae of the classical theta function $\vartheta_3(z)$. The double sum $S(k) := \sum_{h=1}^{k-1}S(h,k)$ has a remarkable distribution of values. Although properties for $S(k)$ and a related sum can be established, several interesting conjectures are open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_03234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Arithmetic Sum Associated with the Classical Theta Function Berndt, Bruce C. Bhat, Raghavendra N. Meyer, Jeffrey L. Xie, Likun Zaharescu, Alexandru Number Theory The sum $S(h,k):=\sum_{j=1}^{k-1}(-1)^{j+1+[hj/k]}$ appears in the modular transformation formulae of the classical theta function $\vartheta_3(z)$. The double sum $S(k) := \sum_{h=1}^{k-1}S(h,k)$ has a remarkable distribution of values. Although properties for $S(k)$ and a related sum can be established, several interesting conjectures are open. |
| title | An Arithmetic Sum Associated with the Classical Theta Function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2501.03234 |