Most Accessed Articles: Research in Number Theoryhttps://resnumtheor.springeropen.comMost Accessed Articles: Research in Number TheoryIrreducible canonical representations in positive characteristichttps://resnumtheor.springeropen.com/articles/10.1007/s40993-015-0004-8For X a curve over a field of positive characteristic, we investigate when the canonical representation of Aut(X) on H 0 (X,Ω X) is irreducible. Any curve with an...Research ArticleFri, 29 May 2015 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-015-0004-8Benjamin Gunby, Alexander Smith and Allen Yuan2015-05-29T00:00:00ZModular forms with large coefficient fields via congruenceshttps://resnumtheor.springeropen.com/articles/10.1007/s40993-015-0003-9We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbit...Research ArticleFri, 29 May 2015 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-015-0003-9Luis Víctor Dieulefait, Jorge Jiménez Urroz and Kenneth Alan Ribet2015-05-29T00:00:00ZThe 1729 K3 surfacehttps://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0058-2We revisit the mathematics that Ramanujan developed in connection with the famous “taxi-cab” number 1729. A study of his writings reveals that he had been studying Euler’s diophantine equationResearchMon, 17 Oct 2016 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0058-2Ken Ono and Sarah Trebat-Leder2016-10-17T00:00:00ZOn powers that are sums of consecutive like powershttps://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0068-0ResearchTue, 14 Feb 2017 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0068-0Vandita Patel and Samir Siksek2017-02-14T00:00:00ZPartition zeta functionshttps://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0039-5We exploit transformations relating generalized q-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such asResearchTue, 15 Mar 2016 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0039-5Robert Schneider2016-03-15T00:00:00Z