By Paul Reynolds
World affairs correspondent, BBC News website
The study says the voting trends in a number of provinces make Mahmoud Ahmadinejad's overwhelming victory questionable
A statistical analysis has now been published to try to support the claim that the opposition in Iran is right to question the declared result.
On the face of it, there seems no reason to doubt the official numbers.
In 2005, in a run-off ballot, Mahmoud Ahmadinejad was elected president with 62% of the vote compared with 36% for his opponent, Akbar Hashemi Rafsanjani.
In 2009, in the first round, President Ahmadinejad was re-elected with 63% of the vote compared with 34% for Mir Hossein Mousavi.
So what is the problem?
According to a study edited by Professor Ali Ansari, of the Institute of Iranian Studies at the University of St Andrews and of the London think tank Chatham House, the problem lies in the increased turnout.
In 2005, Mr Ahmadinejad got 17 million votes and in 2009 he got 24 million.
The question is, where did all those extra votes come from?
The answer, according to this study, is not at all clear.
It examines three factors:
1. Voter turn out
The report says that two provinces showed a turnout of more than 100% and four more of more than 90%.
Regional variations, it says, have disappeared, and there is "no correlation between the increased turn out and the swing to Ahmadinejad. This challenges the notion that Ahmadinejad's victory was due to the massive participation of a previously silent conservative majority."
"If Ahmadinejad's victory was primarily caused by the increase in voter turnout, one would expect the data to show that the provinces where there was the greatest 'swing' in support towards Ahmadinejad would also be the provinces with the greatest increase in voter turnout. This is not the case," it says.
It concludes: "A number of aspects of the reported turnout figures are problematic: the massive increases from 2005; the collapse of regional variations; and the absence of any clear link between increases in turnout and increased support for any one candidate."
2. So where did the new votes come from?
The study examines the results from this year and compares them with the first round from 2005, concluding that there would have to have been a huge swing from previously reform-minded voters into the Ahmadinejad camp.
The study says: "In a third of all provinces, the official results would require that Ahmadinejad took not only all former conservative voters, and all former centrist voters, and all new voters, but also up to 44% of former reformist voters, despite a decade of conflict between these two groups."
You can see the point raised by looking at results from the provinces.
Take Hamedan. In 2005, Mr Ahmadinejad won 195,000 votes. In 2009, it was 765,000 - a difference of 570,000.
If you add to his 2005 vote the others who voted for conservative candidates in that year (97,000) and the non-voters (218,000), you reach only 510,000.
To get to the total declared of 765,000 this year, many reformist voters from 2005 must also have voted for Mr Ahmadinejad.
The report says that, for the official figures to be correct, 24% of former reformist voters must have voted for Mr Ahamdinajed this time.
In Lorestan province, the study estimates that 44% of former reformist voters would have had to have voted for President Ahmadinejad.
Is this possible? Yes. Is it likely? The report doubts it.
3. Do rural voters support Ahmadinejad?
The answer, according to the study, is that the 2005 election showed his support was mainly in urban and suburban areas.
It explains this by saying that "much of Iran's rural population is comprised of ethnic minorities... [with] a history both of voting reformist and of voting for members of their own ethnic group."
The report questions why, in 2009, the data "suggests a sudden shift in political support... showing substantial swings for Ahmadinejad".
It concludes: "This increase in support for Ahmadinejad amongst rural and ethnic minority voters is out of step with previous trends, extremely large in scale, and central to the question of how the credibility of Ahmadinejad's victory has been perceived within Iran."
All this might be suggestive but none of it is conclusive.
Supporters of the Iranian government's declarations will point to the similarities of the percentages compared to the 2005 result.
They also point to an opinion poll carried out during the campaign by Ken Ballen and Patrick Doherty, who reported in the Washington Post on 15 June: "The election results in Iran may reflect the will of the Iranian people.
"Many experts are claiming that the margin of victory of incumbent President Mahmoud Ahmadinejad was the result of fraud or manipulation, but our nationwide public opinion survey of Iranians three weeks before the vote showed Ahmadinejad leading by a more than 2 to 1 margin - greater than his actual apparent margin of victory in Friday's election."
In turn, others have questioned the significance of this poll finding.
Professor Mansoor Moaddel of the University of Michigan pointed out that "key political events occurred between the data gathering and the election" and that "of 1,731 people contacted, well over half either refused to participate (42.2%) or did not indicate a preferred candidate (15.6%)."