Non-Wieferich primes in number fields and a b c -conjecture

Srinivas Kotyada; Subramani Muthukrishnan

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 2, page 445-453
  • ISSN: 0011-4642

Abstract

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Let K / ℚ be an algebraic number field of class number one and let 𝒪 K be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in 𝒪 K under the assumption of the a b c -conjecture for number fields.

How to cite

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Kotyada, Srinivas, and Muthukrishnan, Subramani. "Non-Wieferich primes in number fields and $abc$-conjecture." Czechoslovak Mathematical Journal 68.2 (2018): 445-453. <http://eudml.org/doc/294271>.

@article{Kotyada2018,
abstract = {Let $K/\mathbb \{Q\}$ be an algebraic number field of class number one and let $\mathcal \{O\}_K$ be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in $\mathcal \{O\}_K$ under the assumption of the $abc$-conjecture for number fields.},
author = {Kotyada, Srinivas, Muthukrishnan, Subramani},
journal = {Czechoslovak Mathematical Journal},
keywords = {Wieferich prime; non-Wieferich prime; number field; $abc$-conjecture},
language = {eng},
number = {2},
pages = {445-453},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non-Wieferich primes in number fields and $abc$-conjecture},
url = {http://eudml.org/doc/294271},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Kotyada, Srinivas
AU - Muthukrishnan, Subramani
TI - Non-Wieferich primes in number fields and $abc$-conjecture
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 445
EP - 453
AB - Let $K/\mathbb {Q}$ be an algebraic number field of class number one and let $\mathcal {O}_K$ be its ring of integers. We show that there are infinitely many non-Wieferich primes with respect to certain units in $\mathcal {O}_K$ under the assumption of the $abc$-conjecture for number fields.
LA - eng
KW - Wieferich prime; non-Wieferich prime; number field; $abc$-conjecture
UR - http://eudml.org/doc/294271
ER -

References

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  4. Murty, M. R., Esmonde, J., 10.1007/b138452, Graduate Texts in Mathematics 190, Springer, Berlin (2005). (2005) Zbl1055.11001MR2090972DOI10.1007/b138452
  5. PrimeGrid Project. Available at http://www.primegrid.com/, . 
  6. Silverman, J. H., 10.1016/0022-314X(88)90019-4, J. Number Theory 30 (1988), 226-237. (1988) Zbl0654.10019MR0961918DOI10.1016/0022-314X(88)90019-4
  7. Vojta, P., 10.1007/BFb0072989, Lecture Notes in Mathematics 1239, Springer, Berlin (1987). (1987) Zbl0609.14011MR0883451DOI10.1007/BFb0072989
  8. Wieferich, A., 10.1515/crll.1909.136.293, J. Reine Angew. Math. 136 (1909), 293-302 German 9999JFM99999 40.0256.03. (1909) MR1580782DOI10.1515/crll.1909.136.293

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