Telefonaktiebolaget LM Ericsson (ERIC) 20-F 2004 FY Annual report (foreign)

Exhibit 13.1

Certification of Chief Executive Officer

Pursuant to 18 U.S.C. §1350, as created by Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officer of Telefonaktiebolaget LM Ericsson (publ) (the “Company”) hereby certifies, to such officer’s knowledge, that:

(i) the Annual Report on Form 20-F of the Company for the period ended December 31, 2004 (the “Report”) fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated:March 23, 2005

/s/    CARL-HENRIC SVANBERG        

Carl Henric-Svanberg

President and Chief Executive Officer

The foregoing certification is being furnished solely to accompany the Report pursuant to 18 U.S.C. §1350, and is not being filed for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, and is not to be incorporated by reference into any filing of the Company, whether made before or after the date hereof, regardless of any general incorporation language in such filing.