On simultaneous approximations to the logarithms of primes
M. A. Korolev, I. S. Rezvyakova

References
1.	Kronecker L., “Näherungsweise ganzzahlige Auflösung linearer Gleichungen”, Monats. Königl. Preuss. Akad. Wiss. Berlin, 1884, 1179–1193
2.	Hensel K. (ed.), Leopold Kronecker's Werke, v. III, Teubner, Leipzig, 1899
3.	Hardy G. H., Wright E. M., An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1975
4.	Turán P., “A theorem on diophantine approximation with application to Riemann zeta-function”, Acta Sci. Math. (Szeged), 21 (1960), 311–318
5.	Gonek S. M., Montgomery H. L., “Kronecker's approximation theorem”, Indag. Math. (N.S.), 27:2 (2016), 506–523
6.	Titchmarsh E.K., Teoriya dzeta-funktsii Rimana, M., Izd-vo inostr. lit., 1953
7.	Bohr H., “Again the Kronecker Theorem”, J. Lond. Math. Soc., 9 (1934), 5–6
8.	Konyagin S. V., Korolev M. A., “O yavlenii Titchmarsha v teorii dzeta-funktsii Rimana”, Teoriya priblizhenii, funktsionalnyi analiz i prilozheniya, Sbornik statei. K 70-letiyu akademika Borisa Sergeevicha Kashina, Trudy MIAN, 318, MIAN, M., 2022, 182–201
9.	Besikovitch A. S., “On the linear independence of fractional powers of integers”, J. London Math. Soc., 15 (1940), 3–6
10.	Chandrasekkharan K., Arifmeticheskie funktsii, Nauka, M., 1975
11.	Selberg A., On the remainder term in the lattice point problem of the circle, Manuscript http://publications.ias.edu/selberg/section/2494
12.	Heath-Brown D. R., “The distribution and moments of the error term in the Dirichlet divisor problem”, Acta Arith., 60:4 (1992), 389–415
13.	Korolev M. A., Popov D. A., “Ob integrale Yutily v probleme kruga”, Izv. RAN. Ser. matem., 86:3 (2022), 3–46
14.	Bukhshtab A. A., Teoriya chisel, Uchpedgiz, M., 1960
15.	Mordell L. J., “On the linear independence of algebraic numbers”, Pacific J. Math., 3:3 (1953), 625–630
16.	Khua L.-K., Metod trigonometricheskikh summ i ego primenenie v teorii chisel, Mir, M., 1964