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  1. Content type: Research

    We revisit a statement of Birch that the field of moduli for a marked three-point ramified cover is a field of definition. Classical criteria due to Dèbes and Emsalem can be used to prove this statement in the...

    Authors: Jeroen Sijsling and John Voight

    Citation: Research in Number Theory 2016 2:27

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  2. Content type: Research

    We generalize a result of Garvan on inequalities and interpretations of the moments of the partition rank and crank functions. In particular for nearly 30 Bailey pairs, we introduce a rank-like function, estab...

    Authors: Catherine Babecki, Chris Jennings-Shaffer and Geoffrey Sangston

    Citation: Research in Number Theory 2016 2:35

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  3. Content type: Research

    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...

    Authors: Nickolas Andersen

    Citation: Research in Number Theory 2016 2:32

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  4. Content type: Research

    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...

    Authors: Brian Conrey and Jonathan P. Keating

    Citation: Research in Number Theory 2016 2:24

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  5. Content type: Research

    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...

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

    Citation: Research in Number Theory 2016 2:25

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  6. Content type: Research

    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

    Authors: Ken Ono and Sarah Trebat-Leder

    Citation: Research in Number Theory 2016 2:26

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

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