Most Recent Articles: Research in Number Theoryhttps://resnumtheor.springeropen.comMost Recent Articles: Research in Number TheoryDiophantine triples in linear recurrences of Pisot typehttps://resnumtheor.springeropen.com/articles/10.1007/s40993-018-0121-2The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions...ResearchMon, 25 Jun 2018 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-018-0121-2Clemens Fuchs, Christoph Hutle and Florian Luca2018-06-25T00:00:00ZOn Fermat’s equation over some quadratic imaginary number fieldshttps://resnumtheor.springeropen.com/articles/10.1007/s40993-018-0117-yResearchFri, 04 May 2018 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-018-0117-yGeorge C. Ţurcaş2018-05-04T00:00:00ZOn the arithmetic of simple singularities of type Ehttps://resnumtheor.springeropen.com/articles/10.1007/s40993-018-0110-5An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exceptional diagramsResearchMon, 16 Apr 2018 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-018-0110-5Beth Romano and Jack A. Thorne2018-04-16T00:00:00ZOn the de-Rham cohomology of hyperelliptic curveshttps://resnumtheor.springeropen.com/articles/10.1007/s40993-018-0111-4For any hyperelliptic curve X, we give an explicit basis of the first de-Rham cohomology of X in terms of Čech cohomology. We use this to produce a family of curves in characteristic ...ResearchMon, 02 Apr 2018 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-018-0111-4Bernhard Köck and Joseph Tait2018-04-02T00:00:00ZA new formula for Chebotarev Densitieshttps://resnumtheor.springeropen.com/articles/10.1007/s40993-017-0093-7We give a new formula for the Chebotarev Densities of Frobenius elements in Galois groups. This formula is given in terms of smallest prime factorsResearchThu, 07 Dec 2017 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-017-0093-7Madeline Locus Dawsey2017-12-07T00:00:00Z