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  1. Research

    Linear incongruences for generalized eta-quotients

    For a given generalized eta-quotient, we show that linear progressions whose residues fulfill certain quadratic equations do not give rise to a linear congruence modulo any prime. This recovers known results f...

    Steffen Löbrich

    Research in Number Theory 2017 3:18

    Published on: 9 August 2017

  2. Research

    Artin L-functions of small conductor

    We study the problem of finding the Artin L-functions with the smallest conductor for a given Galois type. We adapt standard analytic techniques to our novel situation of fixed Galois type and obtain much improve...

    John W. Jones and David P. Roberts

    Research in Number Theory 2017 3:16

    Published on: 10 July 2017

  3. 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

  4. 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

  5. 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

  6. 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

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