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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2105.02492 |
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| _version_ | 1866915639602446336 |
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| author | Devin, Lucile |
| author_facet | Devin, Lucile |
| contents | Motivated by questions of Fouvry and Rudnick on the distribution of Gaussian primes, we develop a very general setting in which one can study inequities in the distribution of analogues of primes through analytic properties of infinitely many $L$-functions. In particular, we give a heuristic argument for the following claim : for more than half of the prime numbers that can be written as a sum of two square, the odd square is the square of a positive integer congruent to $1 \bmod 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_02492 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Discrepancies in the distribution of Gaussian primes Devin, Lucile Number Theory Motivated by questions of Fouvry and Rudnick on the distribution of Gaussian primes, we develop a very general setting in which one can study inequities in the distribution of analogues of primes through analytic properties of infinitely many $L$-functions. In particular, we give a heuristic argument for the following claim : for more than half of the prime numbers that can be written as a sum of two square, the odd square is the square of a positive integer congruent to $1 \bmod 4$. |
| title | Discrepancies in the distribution of Gaussian primes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2105.02492 |