Notable activist investor Carl Icahn, chairman of Icahn Enterprises, Thursday published on his new website a letter he wrote to Apple CEO Tim Cook. 

The letter, which was not immediately available due to a technical glitch on the new website, urges Cook to immediately raise the amount of Apple's share buyback to $150 billion. Apple did not immediately comment on the matter. 

In the letter, Icahn praised Apple and its management and said that he thinks the company's current irrational undervaluation is a "short-term anomaly."

Icahn currently owns 4,730,739 shares of Apple, bringing his position in the company to $2.5 billion, which he says reflects his company's belief that the market continues to dramatically undervalue Apple. Icahn says he intends to buy more shares going forward. 

"From our perspective, Apple is the world’s greatest consumer product innovator and has one of the strongest and most respected brand names in history," Icahn wrote. "We consider Apple to be our most compelling investment."

Icahn said that the timing for a larger buyback is still ripe, but added that the opportunity for such a move won't last forever. He said that Apple's current commitment to repurchase $60 billion shares over three years may seem like a large buyback, it is simply not large enough given that Apple currently holds $147 billion of cash on its balance sheet.

Icahn argues that Apple generates more than enough cash flow to service a $150 billion buyback. His math on the results of such a huge initiative concludes that Apple's share price would appreciate to $1,250 per share. 

"If the company decided to borrow the full $150 billion at a 3 percent interest rate to commence a tender at $525 per share, the result would be an immediate 33 percent boost to earnings per share, translating into a 33 percent increase in the value of the shares, which significantly assumes no multiple expansion," Icahn wrote in the letter. "Longer term (in three years) if you execute this buyback as proposed, we expect the share price to appreciate to $1,250, assuming the market rewards EBIT growth of 7.5% per year with a more normal market multiple of 11x EBIT."

Icahn made clear a commitment to Apple for the long-term. 

"Furthermore, to invalidate any possible criticism that I would not stand by this thesis in terms of its long term benefit to shareholders, I hereby agree to withhold my shares from the proposed $150 Billion tender offer. There is nothing short term about my intentions here," he wrote.

Shares of Apple were up a little over 1 percent in morning trading Thursday at $531.57.