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  1. Content type: Research

    The study of Diophantine triples taking values in linear recurrence sequences is a variant of a problem going back to Diophantus of Alexandria which has been studied quite a lot in the past. The main questions...

    Authors: Clemens Fuchs, Christoph Hutle and Florian Luca

    Citation: Research in Number Theory 2018 4:29

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  2. Content type: Research

    An ADE Dynkin diagram gives rise to a family of algebraic curves. In this paper, we use arithmetic invariant theory to study the integral points of the curves associated to the exceptional diagrams

    Authors: Beth Romano and Jack A. Thorne

    Citation: Research in Number Theory 2018 4:21

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  3. Content type: Research

    For any hyperelliptic curve X, we give an explicit basis of the first de-Rham cohomology of X in terms of Čech cohomology. We use this to produce a family of curves in characteristic  ...

    Authors: Bernhard Köck and Joseph Tait

    Citation: Research in Number Theory 2018 4:19

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  4. Content type: Research

    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

    Authors: Madeline Locus Dawsey

    Citation: Research in Number Theory 2017 3:27

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  5. Content type: Research

    We give a complete description of the arboreal Galois representation of a certain postcritically finite cubic polynomial over a large class of number fields and for a large class of basepoints. This is the fir...

    Authors: Robert L. Benedetto, Xander Faber, Benjamin Hutz, Jamie Juul and Yu Yasufuku

    Citation: Research in Number Theory 2017 3:29

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  6. Content type: Research

    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...

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

    Citation: Research in Number Theory 2017 3:25

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  7. Content type: Research

    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...

    Authors: Robert Guralnick and Kiran S. Kedlaya

    Citation: Research in Number Theory 2017 3:22

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  8. Content type: Research

    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...

    Authors: Robert Kottwitz and Preston Wake

    Citation: Research in Number Theory 2017 3:20

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  9. Content type: Research

    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...

    Authors: Steffen Löbrich

    Citation: Research in Number Theory 2017 3:18

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  10. Content type: Research

    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...

    Authors: John W. Jones and David P. Roberts

    Citation: Research in Number Theory 2017 3:16

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  11. Content type: Research

    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.

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

    Citation: Research in Number Theory 2017 3:13

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  12. Content type: Research

    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 ...

    Authors: Ron Evans and John Greene

    Citation: Research in Number Theory 2017 3:8

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