A cabinet minister has been sent two letters from politicians in Brighton and Hove on the issue of council tax.
Councillor Kitcat, the Brighton and Hove City Council cabinet member for finance and central services, wants Mr Pickles to scrap the second home discount.
He said that it was costing the council £177,000 a year.
At the same time Mr Kirby, who represents Brighton Kemptown, and Mr Weatherley, who represents Hove, wrote to Mr Pickles about the student exemption.
Students living in halls of residence or a home occupied only by students are exempt from paying council tax.
There are more than 30,000 students in Brighton and Hove.
As they are not counted as adults for council tax purposes, some contribute to the growing number of properties where a single person discount is being claimed.
Councillor Kitcat said: “Town halls should have the freedom to decide local taxation themselves.
“But while we have no choice but to charge council tax, I believe Brighton and Hove should be given the discretion to stop offering discounts to second home owners.
“The £177,000 this tax discount cost the council this year would have helped tackle inequality and support much-needed services for the young, elderly and vulnerable.
“We’re fighting for a better deal for residents and I’m calling on Eric Pickles as the minister responsible, who believes in localism, to free councils to make their own choices about second home tax discounts.
“I look forward to his response.”
He said that scrapping the discount would help to protect vital services under pressure because of the public spending squeeze.
And it would encourage homes to be brought back into use which would help tackle the desperate shortage of affordable housing in Brighton and Hove.
The two Tory MPs called on the government to clarify its position on student exemptions.
They asked Mr Pickles to say what plans there were to commit money to regularise the situation when the funding powers were decentralised.
In their letter they said: “It is a pressing concern for Brighton and Hove, where the number of students is rocketing.
“More demand is being placed upon council services but no more council tax is being collected.
“If anything, the council collects less council tax with the arrival of each student.
“While it is a boon to the local economy in many respects, the lack of direct funding for our local authority from its own residents is becoming a growing burden.
“Many towns and cities across the country no doubt face this problem, particularly those with large student populations.”