Geodesic
On the convergence exponent of the singular integral in the multi-dimensional analogue of Tarry's problem
Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 405-418

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We obtain upper and lower bounds for the convergence exponent of the singular integral in the many-dimensional analogue of Tarry's problem on the asymptotics of the number of solutions of systems of Diophantine equations. In several cases we establish the exact values of the convergence exponent of the singular integral. 
@article{IM2_2003_67_2_a8,
     author = {M. A. Chahkiev},
     title = {On the convergence exponent of the singular integral in the multi-dimensional analogue of {Tarry's} problem},
     journal = {Izvestiya. Mathematics },
     pages = {405--418},
     publisher = {mathdoc},
     volume = {67},
     number = {2},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a8/}
}
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M. A. Chahkiev. On the convergence exponent of the singular integral in the multi-dimensional analogue of Tarry's problem. Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 405-418. http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a8/