Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Exponents of class groups of real quadratic function fields (II)


Authors: Kalyan Chakraborty and Anirban Mukhopadhyay
Journal: Proc. Amer. Math. Soc. 134 (2006), 51-54
MSC (2000): Primary 11R58; Secondary 11R29
DOI: https://doi.org/10.1090/S0002-9939-05-07953-0
Published electronically: June 13, 2005
MathSciNet review: 2170542
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $g$ be an even positive integer. We show that there are $\gg q^{l/g}/l^2$ polynomials $D\in\mathbb F_q[t]$with $\deg(D)\le l$ such that the ideal class group of the real quadratic extensions $\mathbb F_q(t,\sqrt D)$ have an element of order $g$.


References [Enhancements On Off] (What's this?)

  • 1. Asako Nakamura: Pell's equation on function fields. (in Japanese), Sugaku, 54, no. 3(1995), 308-313. MR 1929899 (2003g:11026)
  • 2. David A. Cardon and M. Ram Murty: Exponents of class groups of quadratic function fields over finite fields, Canadian Math. Bulletin, Vol.44 (2001), no. 4, 398-407. MR 1863632 (2002g:11164)
  • 3. Kalyan Chakraborty and Anirban Mukhopadhyay: Exponents of class groups of real quadratic function fields, Proc. Amer. Math. Soc. 132 (2004), 1951-1955. MR 2053965 (2005a:11182)
  • 4. Christian Friesen : Class number divisibility in real quadratic function fields, Canad. Math. Bull., Vol.35(3), (1992), 361-370. MR 1184013 (93h:11130)
  • 5. Christian Friesen and Paul van Wamelen: Class numbers of real quadratic function fields, Acta Arith. 81 (1997), no. 1, 45-55. MR 1454155 (98d:11141)
  • 6. K. Chakraborty and M. Ram Murty: On the number of real quadratic fields with class number divisible by $3$, Proc. Amer. Math. Soc. 131 (2002), no. 1, 41-44. MR 1929021 (2003m:11184)
  • 7. Florian Luca: A note on the divisibility of class numbers of real quadratic fields, C. R. Math. Acad. Sci. Soc. R. Can. 25 (2003), no. 3, 71-75. MR 1999181 (2004g:11099)
  • 8. M. Ram Murty: Exponents of class groups of quadratic fields, Topics in Number Theory (University Park, PA, 1997), Math. Appl. 467, Kluwer Acad. Publ., Dordrecht, (1999), 229-239. MR 1691322 (2000b:11123)
  • 9. Michael Rosen: Number Theory in Function Fields, Graduate Texts in Mathematics, 210. Springer-Verlag, 2002. MR 1876657 (2003d:11171)
  • 10. Gang Yu: A note on the divisibility of class numbers of real quadratic fields, J. Number Theory 97 (2002), 35-44. MR 1939135 (2003m:11187)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11R58, 11R29

Retrieve articles in all journals with MSC (2000): 11R58, 11R29


Additional Information

Kalyan Chakraborty
Affiliation: Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211 019, India
Email: kalyan@mri.ernet.in

Anirban Mukhopadhyay
Affiliation: Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai 600 113, India
Email: anirban@imsc.res.in

DOI: https://doi.org/10.1090/S0002-9939-05-07953-0
Keywords: Class group, real quadratic fields
Received by editor(s): March 26, 2004
Received by editor(s) in revised form: August 27, 2004
Published electronically: June 13, 2005
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society