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  1. 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

  2. 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

  3. 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

  4. 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

  5. Research Article

    Mean values of multiplicative functions over function fields

    We 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 ...

    Andrew Granville, Adam J. Harper and Kannan Soundararajan

    Research in Number Theory 2015 1:25

    Published on: 21 December 2015

  6. Research

    A correspondence of modular forms and applications to values of L-series

    A interpretation of the Rogers–Zudilin approach to the Boyd conjectures is established. This is based on a correspondence of modular forms which is of independent interest. We use the reinterpretation for two ...

    Nikolaos Diamantis, Michael Neururer and Fredrik Strömberg

    Research in Number Theory 2015 1:27

    Published on: 21 December 2015

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