Exponents of class groups of real quadratic function fields (II)
HTML articles powered by AMS MathViewer
- by Kalyan Chakraborty and Anirban Mukhopadhyay
- Proc. Amer. Math. Soc. 134 (2006), 51-54
- DOI: https://doi.org/10.1090/S0002-9939-05-07953-0
- Published electronically: June 13, 2005
- PDF | Request permission
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
- Asako Nakamura, Pell’s equation on function fields, Sūgaku 54 (2002), no. 3, 308–313 (Japanese). MR 1929899
- David A. Cardon and M. Ram Murty, Exponents of class groups of quadratic function fields over finite fields, Canad. Math. Bull. 44 (2001), no. 4, 398–407. MR 1863632, DOI 10.4153/CMB-2001-040-0
- Kalyan Chakraborty and Anirban Mukhopadhyay, Exponents of class groups of real quadratic function fields, Proc. Amer. Math. Soc. 132 (2004), no. 7, 1951–1955. MR 2053965, DOI 10.1090/S0002-9939-04-07269-7
- Christian Friesen, Class number divisibility in real quadratic function fields, Canad. Math. Bull. 35 (1992), no. 3, 361–370. MR 1184013, DOI 10.4153/CMB-1992-048-5
- Christian Friesen and Paul van Wamelen, Class numbers of real quadratic function fields, Acta Arith. 81 (1997), no. 1, 45–55. MR 1454155, DOI 10.4064/aa-81-1-45-55
- K. Chakraborty and M. Ram Murty, On the number of real quadratic fields with class number divisible by 3, Proc. Amer. Math. Soc. 131 (2003), no. 1, 41–44. MR 1929021, DOI 10.1090/S0002-9939-02-06603-0
- 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 (English, with French summary). MR 1999181
- M. Ram Murty, Exponents of class groups of quadratic fields, Topics in number theory (University Park, PA, 1997) Math. Appl., vol. 467, Kluwer Acad. Publ., Dordrecht, 1999, pp. 229–239. MR 1691322
- Michael Rosen, Number theory in function fields, Graduate Texts in Mathematics, vol. 210, Springer-Verlag, New York, 2002. MR 1876657, DOI 10.1007/978-1-4757-6046-0
- Gang Yu, A note on the divisibility of class numbers of real quadratic fields, J. Number Theory 97 (2002), no. 1, 35–44. MR 1939135, DOI 10.1006/jnth.2001.2773
Bibliographic 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
- 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
- © Copyright 2005 American Mathematical Society
- 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
- MathSciNet review: 2170542