Bounded gaps between primes in Chebotarev sets
J Thorner - Research in the Mathematical Sciences, 2014 - Springer
Purpose A new and exciting breakthrough due to Maynard establishes that there exist
infinitely many pairs of distinct primes p 1, p 2 with| p 1-p 2|≤ 600 as a consequence of the …
infinitely many pairs of distinct primes p 1, p 2 with| p 1-p 2|≤ 600 as a consequence of the …
Non-vanishing theorems for quadratic twists of elliptic curves
S Zhai - arXiv preprint arXiv:1409.0231, 2014 - arxiv.org
In this paper, we show that, by applying some results on modular symbols, for a family of
certain elliptic curves defined over $\mathbb Q $, there is a large class of explicit quadratic …
certain elliptic curves defined over $\mathbb Q $, there is a large class of explicit quadratic …
Quadratic twists of genus one curves and Diophantine quintuples
M Kazalicki - arXiv preprint arXiv:2209.12864, 2022 - arxiv.org
Motivated by the theory of Diophantine $ m $-tuples, we study rational points on quadratic
twists $ H^ d: dy^ 2=(x^ 2+ 6x-18)(-x^ 2+ 2x+ 2) $, where $| d| $ is a prime. If we denote by …
twists $ H^ d: dy^ 2=(x^ 2+ 6x-18)(-x^ 2+ 2x+ 2) $, where $| d| $ is a prime. If we denote by …
Bounded gaps between products of special primes
PN Chung, S Li - Mathematics, 2014 - mdpi.com
In their breakthrough paper in 2006, Goldston, Graham, Pintz and Yıldırım proved several
results about bounded gaps between products of two distinct primes. Frank Thorne …
results about bounded gaps between products of two distinct primes. Frank Thorne …
Congruent numbers and congruences between half-integral weight modular forms
M Kazalicki - Journal of number theory, 2013 - Elsevier
In this paper we investigate 2-parts of class numbers of quadratic imaginary field Q (− d) and
2-parts of the algebraic parts of the central L-values associated to the elliptic curves Ed: y2 …
2-parts of the algebraic parts of the central L-values associated to the elliptic curves Ed: y2 …