Geodesic
On the Multiplicative Properties Modulo~$m$ of Numbers with Missing Digits
Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 385-404

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We obtain upper bounds for character sums modulo a composite number over sets of numbers with missing digits in a number system. We derive results on the solvability of congruences of the form $x_1\dotsb x_t\equiv\lambda\pmod{m}$ in the numbers with missing digits and also asymptotic formulas for the number of solutions.
Keywords: number system, number with missing digits, character sum, finite Fourier series. 
@article{MZM_2007_81_3_a7,
     author = {N. G. Moshchevitin and I. D. Shkredov},
     title = {On the {Multiplicative} {Properties} {Modulo~}$m$ of {Numbers} with {Missing} {Digits}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {385--404},
     publisher = {mathdoc},
     volume = {81},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a7/}
}
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N. G. Moshchevitin; I. D. Shkredov. On the Multiplicative Properties Modulo~$m$ of Numbers with Missing Digits. Matematičeskie zametki, Tome 81 (2007) no. 3, pp. 385-404. http://geodesic.mathdoc.fr/item/MZM_2007_81_3_a7/