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math.NT2018
Refined Goldbach conjectures with primes in progressions
Kimball Martin
We formulate some refinements of Goldbach's conjectures based on heuristic arguments and numerical data. For instance, any even number greater than 4 is conjectured to be a sum of…
math.NT2018★ 6 cited
The basis problem revisited
Kimball Martin
We explicitly describe the Jacquet-Langlands correspondence at the level of modular forms. This gives a simpler and more flexible solution to Eichler's basis problem for general le…
math.NT2018★ 2 cited
Rationality of Darmon points over genus fields of non-maximal orders
Matteo Longo, Kimball Martin, Yan Hu
Stark-Heegner points, also known as Darmon points, were introduced by H. Darmon as certain local points on rational elliptic curves, conjecturally defined over abelian extensions o…