DIOPHANTINE INEQUALITIES OF FRACTIONAL DEGREE

This paper is concerned with the study of diagonal Diophantine inequalities fractional degree θ, where θ > 2 real and non-integral. For fixed non-zero numbers λ i not all same sign, we write F ( x ) = 1 + ⋯ s . a positive number τ, give an asymptotic formula for integer solutions inequality | < τ inside box side length P. Moreover, investigate problem representing large by definite generalised polynomial above shape. A key result in our approach essentially optimal mean value estimate exponential sums involving powers integers.