"K" is either a plate ID or part of the serial number. In either case it's not a determining factor in the bill's value. What matters is what letter if any appears next to the date. There may not be a letter, or a small A or B.
However, regardless of whether you have a 1957, 1957A, or 1957B bill, all of these are very common among collectors and retail for at most $1.50 in circulated condition.
1957 is the most common series for $1 silver certificates. Starting with a K adds no extra value. They're worth $2 to $3 on average.
Please check your bill again. There were no series letters on 1934 silver certificates, and no silver certificate series letters ever went as high as K. Please see the question "What is the value of a 1934 US 1 dollar silver certificate?" for more information.
As you may have noted from many other posts on this site, a bill's serial number normally affects its value only when it is a special pattern or low number. Silver certificates were saved in large quantities when they were replaced with Federal Reserve Notes, so yours remains pretty common. It might be worth $1.25 to $3.00 depending on condition.
K. Muraleedharan was born in 1957.
Caroline K was born in 1957.
The "k" in 925k silver does not refer to the purity of the silver. Silver is typically measured in terms of fineness, so 925k silver actually refers to 92.5% pure silver, which is commonly known as sterling silver.
Glenn K. Rieth was born in 1957.
George K. Cockerill died in 1957.
K. C. Chan was born in 1957.
James K. Bredar was born in 1957.
K's Merchandise Mart was created in 1957.
Juha K. Tapio was born in 1957.