On the irregular primes with respect to Euler polynomials

Su Hu; Min-Soo Kim; Min Sha

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arXiv · 1510.01558

On the irregular primes with respect to Euler polynomials

Su Hu·Min-Soo Kim·Min Sha

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Abstract

An odd prime $p$ is called irregular with respect to Euler polynomials if it divides the numerator of one of the numbers $$E_1(0),E_{3}(0),\ldots,E_{p-2}(0),$$ where $E_n(x)$ is the $n$-th Euler polynomial. As in the classical case, we link the regularity of primes to the divisibility of some class numbers. Besides, we obtain some results on the distribution of such irregular primes. Remark: This preprint has been withdrawn, because all the results in it have been included or improved in a recent preprint. (See arXiv:1809.08431).

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Su Hu, Min-Soo Kim, Min Sha. 2015-10-06. On the irregular primes with respect to Euler polynomials. https://arxiv.org/abs/1510.01558

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