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  1. Research

    Faltings heights of CM elliptic curves and special Gamma values

    In this paper, we evaluate the Faltings height of an elliptic curve with complex multiplication by an order in an imaginary quadratic field in terms of Euler’s Gamma function at rational arguments.

    Adrian Barquero-Sanchez, Lindsay Cadwallader, Olivia Cannon, Tyler Genao and Riad Masri

    Research in Number Theory 2017 3:13

    Published on: 5 June 2017

  2. Research

    Some mixed character sum identities of Katz II

    A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime http://static-content.springer.com/image/art%3A10.1007%2Fs40993-016-0071-5/40993_2016_71_Article_IEq1.gif ...

    Ron Evans and John Greene

    Research in Number Theory 2017 3:8

    Published on: 3 April 2017

  3. Research

    On explicit descent of marked curves and maps

    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...

    Jeroen Sijsling and John Voight

    Research in Number Theory 2016 2:27

    Published on: 13 December 2016

  4. 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

  5. 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

  6. 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

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