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arxiv 1112.4945 v6 pith:AFPW7PO3 submitted 2011-12-21 math.NT

Hershy Kisilevsky , Michael O. Rubinstein This is my paper · ORCID
classification math.NT
keywords classesfinitenumberprimeprimesrealizedallowcannot
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We consider the problem of determining whether a set of primes, or, more generally, prime ideals in a number field, can be realized as a finite union of residue classes, or of Frobenius conjugacy classes. We give criteria for a set to be realized in this manner, and show that the subset of primes consisting of every other prime cannot be expressed in this way, even if we allow a finite number of exceptions.

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  1. Infinitely many elliptic curves over $\mathbb{Q}(i)$ with rank 2 and $j$-invariant 1728

    math.NT 2025-06 conditional novelty 7.0 of 10

    Infinitely many genuinely defined elliptic curves over Q(i) of j-invariant 1728 have rank exactly 2.

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