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...Fri, 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...Fri, 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 equationMon, 17 Oct 2016 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0058-2Ken Ono and Sarah Trebat-Leder2016-10-17T00:00:00ZPartition 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 asTue, 15 Mar 2016 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-016-0039-5Robert Schneider2016-03-15T00:00:00ZMean values of multiplicative functions over function fieldshttps://resnumtheor.springeropen.com/articles/10.1007/s40993-015-0023-5We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical ...Mon, 21 Dec 2015 00:00:00 GMThttps://resnumtheor.springeropen.com/articles/10.1007/s40993-015-0023-5Andrew Granville, Adam J. Harper and Kannan Soundararajan2015-12-21T00:00:00Z