In his notifications of geographical situation of medieval India, he do not mention the name of the king of Tamilnadu. Instead of Rajendra, he notifies JAUR as the king of the southern regions starts below odravisaya upto rameswar...
Scholars who are analyzing this notification rubbed their forehead with the words " how this JAUR could mean Rajendra " and some scholars says JAUR as Chola...
While checking with his other wordings we could see the names of other kings like Bhojaraja and Gangeya... But alberuni omits Rajendra's name...
A translation of this term JAUR could give some hints to relate that, what alberuni notifies?
If any one knows Arabic language pls translate this term...
Might be a persianized/arabianized version of ra[JA-RA]a.. You never know..
Rajaraja was LochaLocha for the chinese.. Sadayavarman Vira Pandiyan was 'Asciar' for Marco Polo!!(I couldnt comprehend that in my wildest imagination)!
Thats what happens to tamil names coming from foreign tongues!
Alberuni's notifications about Tamilnadu is veryscanty...
As it has been translated by Edward Sachu, some scholars says there are some mis-translations also. but Sri.K.AN, in his Foreign Notices of South Indiagives the sametranslationaboutsouthindia...
As you said, In Lighter vein - Jaur may be the shorter form of ThanJAUR,
But alberuni says something about the capital of Chola empire or the Jaur's Possessions as follows,
Thence the coast-line comes to the country Laran,in which lies the city of Jimur, then to Vallabha,Kanji, Darvad. Next follows a great bay in whichSingaldib lies, i.e. the island Sarandib (Ceylon). roundthe bay lies the city of Panjayavar (sic). When thiscity had fallen into ruins, the king Jaur, built insteadof it, on the coast towards the west, a new city whichhe called Padnar.
Edward Sachu, the translator of Alberuni's India says " Panjayavar may be a mistake of Tanjore "...
According to these words Padnar shouldnotify the GKC... But,alberuni has used the term Ganges no.of times in his work, If he wishedto notify the GKC, he could use the words related with ganges...
the earliest date of GKC, as I have noticed in the inscriptions which are accessible by me, is Rajendra chola's 15th year (i.e) 1026-27....
Alberuni's work was done in the year 1030 CE or 421 AH.
Accordingly, he says upto Rameswar only, the posseission of Jaur... (i.e)Srilanka was not included... Alberuni may be unaware about Srilanka's Inclusion...
Alberuni's Panjayavar and Padnar may notindicate TANJORE and GKC... probably a Transliteration only....