2026/07/28 by Karimjon Ibrohimjonovich Mirzoabdughafurov
#math.NT
This paper considers Waring's problem for seventeen biquadrates with almost equal summands. We study the number of representations of a sufficiently large natural number N as a sum of seventeen fourth powers of integers lying in a short interval about a common center. Using the Hardy--Littlewood circle method and a refined estimate for a short quartic exponential sum in an intermediate range of rational approximations, we prove an asymptotic formula for a shorter interval than was previously known. The result improves the previously known lower bound for H in Waring's problem for seventeen almost equal fourth powers.