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  1. Research

    Vector-valued modular forms and the mock theta conjectures

    The mock theta conjectures are ten identities involving Ramanujan’s fifth-order mock theta functions. The conjectures were proven by Hickerson in 1988 using q-series methods. Using methods from the theory of harm...

    Nickolas Andersen

    Research in Number Theory 2016 2:32

    Published on: 25 November 2016

  2. Research

    Moments of zeta and correlations of divisor-sums: IV

    In this series we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper begi...

    Brian Conrey and Jonathan P. Keating

    Research in Number Theory 2016 2:24

    Published on: 21 November 2016

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

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