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Creators/Authors contains: "Howe, Everett"

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  1. (, Research in Number Theory)
    Free, publicly-accessible full text available March 1, 2026
  2. ; ; ; ; ; ; ; (, Mathematics of Computation)
    Abstract. We study the extent to which curves over ļ¬nite ļ¬elds are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C ā€² are curves over a ļ¬nite ļ¬eld K, with K-rational base points P and P ā€² , and let D and D ā€² be the pullbacks (via the Abelā€“Jacobi map) of the multiplication-by-2 maps on their Jacobians. We say that (C, P) and (C ā€² , P ā€² ) are doubly isogenous if Jac(C) and Jac(C ā€² ) are isogenous over K and Jac(D) and Jac(D ā€² ) are isogenous over K. For curves of genus 2 whose automorphism groups contain the dihedral group of order eight, we show that the number of pairs of doubly isogenous curves is larger than naĀØıve heuristics predict, and we provide an explanation for this phenomenon. 
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  3. ; (, Research in Number Theory)
    Abstract We show that for every integer$$m > 0$$ m > 0 , there is an ordinary abelian variety over $${{\mathbb {F}}}_2$$ F 2 that has exactlymrational points. 
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  4. ; ; (, Open Book Series)
    null (Ed.)
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