K. G. Gasarian, N. G. Shuppe, A. S. Kulminskaia.** The synthesis of RNA in the presence of small doses of actinomycin . . . . . . . . . . . . . . . 1411
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Submitted 1965-01-01 | RussiaRxiv: ru-196501.91163 | Translated from Russian

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BIOCHEMISTRY

K. G. Gasarian, N. G. Shuppe, A. S. Kulminskaia. The synthesis of RNA in the presence of small doses of actinomycin . . . . . . . . . . . . . . . 1411

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LETTER TO THE EDITOR

The following corrections must be made in my article (L. P. Usol’tsev, “On an exponential rational trigonometric sum of a special form”), published in Dokl. Akad. Nauk, vol. 151, no. 1, 1963.

In estimating the remainder term in the formula of Theorem 2, an erroneous reference was made (p. 63, line 7 from the bottom) to the lemma cited in the text. Instead of this reference, the following argument should be given.

To each system \(x_1,\ldots,x_n\) there will correspond \(O(c^n)\) systems \(y_1,\ldots,y_n\); indeed, if to the system \(x_1,\ldots,x_n\) there corresponds some system \(y_1,\ldots,y_n\), then to this system \(x_1,\ldots,x_n\), in view of the condition \(g^\tau=p+1\), there will correspond no more than \(c^n\) systems of the form \(\tilde y_1+k_1\tau,\ldots,\tilde y_n+k_n\tau\), where \(0\le k_i\le c-1\), and \(\tilde y_i\) is the least nonnegative residue of the number \(y_i\) modulo \(\tau\). Thus, the number of solutions of congruence (1) belonging to the first category is estimated as \(O(c^{n+1}h^{-1})\).

Printed Should read
P. 62, lines 15, 18, 19 from the top and 8 and 10 from the bottom, and p. 64, line 8 from the bottom \(c\tau\to\infty\)
\(1/c\tau\)
\(\tau\to\infty\)
\(1/\tau\)
P. 64, line 7 from the bottom
P. 62, line 7 from the bottom and p. 64, line 7 from the bottom \(c^{n+1}h^{n-1}\) \(c^n h^{n-1}\)

L. Usol’tsev

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Submission history

K. G. Gasarian, N. G. Shuppe, A. S. Kulminskaia.** The synthesis of RNA in the presence of small doses of actinomycin . . . . . . . . . . . . . . . 1411