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  1. Research

    Explicit computations of Hida families via overconvergent modular symbols

    In Pollack and Stevens (Ann Sci Éc Norm Supér 44(1):1–42, 2011), efficient algorithms are given to compute with overconvergent modular symbols. These algorithms then allow for the fast computation of p-adic L-fun...

    Evan P. Dummit, Márton Hablicsek, Robert Harron, Lalit Jain, Robert Pollack and Daniel Ross

    Research in Number Theory 2016 2:25

    Published on: 14 November 2016

  2. Research

    The 1729 K3 surface

    We 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 equation

    Ken Ono and Sarah Trebat-Leder

    Research in Number Theory 2016 2:26

    Published on: 17 October 2016

    The Erratum to this article has been published in Research in Number Theory 2017 3:12

  3. Research

    Criteria for the existence of cuspidal theta representations

    Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal ...

    Solomon Friedberg and David Ginzburg

    Research in Number Theory 2016 2:16

    Published on: 8 August 2016

  4. Research

    Quantum mock modular forms arising from eta–theta functions

    In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta–theta functions by constructing mock modular forms from the eta–theta functions with even character...

    Amanda Folsom, Sharon Garthwaite, Soon-Yi Kang, Holly Swisher and Stephanie Treneer

    Research in Number Theory 2016 2:14

    Published on: 8 August 2016

  5. Research

    Partition zeta functions

    We 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 as

    Robert Schneider

    Research in Number Theory 2016 2:9

    Published on: 15 March 2016

  6. Research

    Divisibility properties of sporadic Apéry-like numbers

    In 1982, Gessel showed that the Apéry numbers associated to the irrationality of ζ(3) satisfy Lucas congruences. Our main result is to prove corresponding congruences for all known sporadic Apéry-like sequences. ...

    Amita Malik and Armin Straub

    Research in Number Theory 2016 2:5

    Published on: 14 February 2016

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