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March 2017 Family of elliptic curves with good reduction everywhere over number fields of given degree
Nao Takeshi
Funct. Approx. Comment. Math. 56(1): 61-65 (March 2017). DOI: 10.7169/facm/1591

Abstract

We show that for Dirichlet characters $\chi_1,\ldots ,\chi_s$ mod $p^m$ the sum $$ \mathop{\sum_{x_1=1}^{p^m} \dots \sum_{x_s=1}^{p^m}}_{ A_1x_1^{k_1}+\dots+ A_sx_s^{k_s}\equiv B \text{ mod } p^m}\chi_1(x_1)\cdots \chi_s(x_s), $$ has a simple evaluation when $m$ is sufficiently large.

Citation

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Nao Takeshi. "Family of elliptic curves with good reduction everywhere over number fields of given degree." Funct. Approx. Comment. Math. 56 (1) 61 - 65, March 2017. https://doi.org/10.7169/facm/1591

Information

Published: March 2017
First available in Project Euclid: 27 January 2017

zbMATH: 06864146
MathSciNet: MR3629011
Digital Object Identifier: 10.7169/facm/1591

Subjects:
Primary: 11G05, 14H52
Secondary: 11R04

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.56 • No. 1 • March 2017
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