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  1. Research

    A new formula for Chebotarev Densities

    We give a new formula for the Chebotarev Densities of Frobenius elements in Galois groups. This formula is given in terms of smallest prime factors http://static-content.springer.com/image/art%3A10.1007%2Fs40993-017-0093-7/40993_2017_93_Article_IEq1.gif

    Madeline Locus Dawsey

    Research in Number Theory 2017 3:27

    Published on: 7 December 2017

  2. Research

    One-level density for holomorphic cusp forms of arbitrary level

    In 2000 Iwaniec, Luo, and Sarnak proved for certain families of L-functions associated to holomorphic newforms of square-free level that, under the Generalized Riemann Hypothesis, as the conductors tend to infini...

    Owen Barrett, Paula Burkhardt, Jonathan DeWitt, Robert Dorward and Steven J. Miller

    Research in Number Theory 2017 3:25

    Published on: 5 December 2017

  3. Research

    Endomorphism fields of abelian varieties

    We give a sharp divisibility bound, in terms of g, for the degree of the field extension required to realize the endomorphisms of an abelian variety of dimension g over an arbitrary number field; this refines a r...

    Robert Guralnick and Kiran S. Kedlaya

    Research in Number Theory 2017 3:22

    Published on: 6 November 2017

  4. Research

    Primitive elements for p-divisible groups

    We introduce the notion of primitive elements in arbitrary truncated p-divisible groups. By design, the scheme of primitive elements is finite and locally free over the base. Primitive elements generalize the “po...

    Robert Kottwitz and Preston Wake

    Research in Number Theory 2017 3:20

    Published on: 8 September 2017

  5. 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

  6. 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

  7. 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

  8. 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

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