Panda, Corina B.
(2020)
*A generalization of a theorem of Hecke for SL_2(F_p) to fundamental discriminants.*
Journal of Number Theory, 207
.
pp. 83-109.
ISSN 0022-314X.
https://resolver.caltech.edu/CaltechAUTHORS:20190523-160733231

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20190523-160733231

## Abstract

Let p > 3 be an odd prime, p ≡ 3 mod 4 and let π+, π− be the pair of cuspidal representations of SL_2(F_p). It is well known by Hecke that the difference m_π+ −m_π− in the multiplicities of these two irreducible representations occurring in the space of weight 2 cusps forms with respect to the principal congruence subgroup Γ(p), equals the class number h(−p) of the imaginary quadratic field Q(√−p). We extend this result to all fundamental discriminants −D of imaginary quadratic fields Q(√−D) and prove that an alternating sum of multiplicities of certain irreducibles of SL_2(Z/DZ) is an explicit multiple, up to a sign and a power of 2, of either the class number h(−D) or of the sums h(−D)+h(−D/2), h(−D)+2h(−D/2); the last two possibilities occur in some of the cases when D ≡ 0 mod 8. The proof uses the holomorphic Lefschetz number.

Item Type: | Article | ||||||
---|---|---|---|---|---|---|---|

Related URLs: |
| ||||||

Alternate Title: | A generalization of a theorem of Hecke for SL2(Fp) to fundamental discriminants | ||||||

Additional Information: | © 2019 Elsevier Inc. Received 5 August 2016, Revised 15 October 2018, Accepted 28 April 2019, Available online 23 May 2019. | ||||||

Subject Keywords: | Hecke; Class number; Ffundamental discriminant; Imaginary quadratic field; Lefschetz number; Fixed points; Modular curve | ||||||

Record Number: | CaltechAUTHORS:20190523-160733231 | ||||||

Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190523-160733231 | ||||||

Official Citation: | Corina B. Panda, A generalization of a theorem of Hecke for SL2(Fp) to fundamental discriminants, Journal of Number Theory, Volume 207, 2020, Pages 83-109, ISSN 0022-314X, https://doi.org/10.1016/j.jnt.2019.04.009. (http://www.sciencedirect.com/science/article/pii/S0022314X19301490) | ||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||

ID Code: | 95772 | ||||||

Collection: | CaltechAUTHORS | ||||||

Deposited By: | Tony Diaz | ||||||

Deposited On: | 23 May 2019 23:17 | ||||||

Last Modified: | 15 Oct 2019 16:36 |

Repository Staff Only: item control page