c 2006 RAS(DoM) and LMS

Russian Math. Surveys 61:5 971–973
Uspekhi Mat. Nauk 61:5 173–175

DOI 10.1070/RM2006v061n05ABEH004359

Kirill Andreevich Rodosskii(obituary)
Professor Kirill Andreevich Rodosskii, doctor of the physical and mathematical sciences,passed away in his 92nd year of life on 30 August
2004, after a long and severe illness.
He was born on 25 February 1913 in
St. Petersburg. Upon finishing secondary school
in 1930 he started working at the October
Chemical Industrial Complex in Leningrad.
After the assassination of S. M. Kirov in December 1934, the political trials and repression
began. In March 1935 the Rodosskii family wasaccused of anti-Soviet agitation and exiled forfive years to Saratov.
In those hard times Rodosskii, while working as an accountant, did not forget his passion
for chess: he became the champion of Saratov
Province. Furthermore, he continued his independent study of mathematics, which
had attracted him since childhood. His uncommon diligence, resolve, and natural
gifts helped him in 1936 to be admitted immediately to the second year of study
in the Faculty of Physics and Mathematics at Saratov State University.
On graduating in 1940 he worked as an assistant in the Department of Mathematical Analysis. But after the creation in the same year of the Department ofAlgebra and Number Theory headed by the well-known scholar Professor Nikolai
Grigor’evich Chudakov, who had been his first teacher, Rodosskii transferred tothat department.
In 1942 he was conscripted into the army, but soon was demobilized because of aserious illness and sent to work as a secondary-school teacher in the village of Strigaiin Saratov Province. Then from May of 1944 he performed non-combatant service in
one of the Building and Erection Directorates in Saratov, where he worked as a tutorof young workers who had gone through industrial training.
After demobilization in 1945 Rodosskii again began working in his profession:
first in the Saratov Economics Institute, then as a researcher in one of the scientificresearch institutes, and from 1949 once more in the Department of Algebra andNumber Theory of Saratov State University.
In 1947 he defended his Ph.D. dissertation “Distribution of the prime numbers
in short arithmetic progressions”. And in 1954 he defended his D.Sc. dissertation“On zeros of L-functions and prime numbers” in the Steklov Mathematical InstituteAMS 2000 Mathematics Subject Classification. 01A70.

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Kirill Andreevich Rodosskii

of the Academy of Sciences of the USSR. Academician Yu. V. Linnik regarded hisdissertation as “superb, outstanding”.
In 1959 Rodosskii became head of the Department of Algebra and Geometry in
the Faculty of Mathematics and Mechanics at Voronezh University.
In 1967 he moved to the Voronezh Pedagogical Institute, where he headed theDepartment of Algebra and Geometry up to 1975. In subsequent years he continued
to work as a professor in this department.
His circle of research interests was distinguished by its breadth. His first papers
involved the distribution of the prime numbers in arithmetic progressions kn + l,
where n 6 N , and l and k are mutually prime numbers with k growing together
with N . The concept of a short arithmetic progression was introduced by Rodosskii
and became generally known.
Rodosskii obtained an asymptotic formula for the number of primes less thanx belonging to the indicated progression as x → ∞ with sufficiently large valuesof k. Moreover, for a finite difference of the Chebyshev function regarded on shortarithmetic progressions he obtained an asymptotic formula which complemented
results of Chudakov in connection with this problem. He proved also that theasymptotic approximation of the Chebyshev function fairly often has a very small
error.
In a number of papers of Soviet and foreign mathematicians beginning in the1930s it was shown that to solve certain problems on the distribution of the prime
numbers it was sufficient to know only the ‘density of the zeros’ falling in theso-called ‘critical strip’ for the Dirichlet L-functions. In a joint paper with Chudakov in 1949 Rodosskii gave a survey of fundamental results obtained with the helpof properties of the density of the zeros. One of the problems discussed there was
the problem of the smallest prime number p(k, l) in an arithmetic progression. The
Hungarian mathematician P. Turán showed that p(k, l) < k c , where c is an absolute
constant independent of k. Turán’s proof was based on a then-unproved hypothesis about the density of the distribution of the zeros of Dirichlet L-functions withcharacters with a single modulus in the critical strip. Linnik proved the inequality
for p(k, l) without using this hypothesis. However, his proof was complicated andlaborious. Rodosskii found a new and simpler proof of the inequality. The latter
proof is in Chapter X of the book Primzahlverteilung by the Austrian mathematician K. Prachar (translated to Russian in 1967). A second proof of Linnik’s theorem
was obtained seven years later by Turán.
Number theory experts were particularly interested in Rodosskii’s paper “On theexceptional zero”, in which a simpler proof was obtained for the famous theoremof the German mathematician C. Siegel on the exceptional zero of L-functions.
Rodosskii subsequently wrote some papers in which he used one of two analytic methods: the method of transformation of ‘weighted sums’ and the methodof transformation of generating functions with the help of an integral expressing
a normal probability distribution. By his first method he was able to get essentially improved estimates of certain trigonometric sums. The second method wassubsequently used effectively in papers by the Hungarian mathematician I. Kátai.
Rodosskii solved some problems in integer programming that had arisen in the theory of the circulation of money and were posed by Professor P. A. Parfan’yak at
the Saratov Economics Institute already in 1947.

Kirill Andreevich Rodosskii

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In the 1970s Rodosskii studied problems in the theory of Euclidean rings andproblems of factorization in commutative rings. The results of years of investigations were published in his monograph The Euclidean algorithm, the first systematicexposition (in the world mathematical literature) of the theory of classical Euclideanrings, with applications to systems of linear equations and linear congruences overEuclidean rings.
He devoted much attention to his pedagogical work. Rodosskii was a brilliant
teacher. His lectures remained long in the memories of his students. He lectured onlinear algebra, number theory, and mathematical logic, gave various special courses,
and guided the research of undergraduate and graduate students and teachers. In1973 he was awarded an honorary diploma by the Ministry of Education of theRussian Soviet Federated Socialist Republic (RSFSR) and the Republican Committee of the Professional Union of University and Research Institute Workers ofthe RSFSR.
Rodosskii performed many tasks of public service. He was editor-in-chief of aninter-university collection of papers on number theory, a member of the Academic
Council of the Central Directorate of Higher Educational Institutions in the Ministry of Education of the RSFSR, and a reviewer of articles and books at the requestof the publishing house “Prosveshchenie” (Education) and the Steklov Mathematical Institute.
Kirill Andreevich Rodosskii was an exceptionally noble, intelligent, and steadfast
man who was kind to all. A bright memory of him will always be preserved in thehearts of those who knew him.
R. A. Arkhontova, A. G. Baskakov, I. A. Bakhtin, È. S. Belyaeva,Yu. G. Borisovich, A. S. Grinenko, V. R. Zachepa,A. A. Karatsuba, A. F. Kudinov, V. V. Obukhovskii, A. I. Perov,
A. S. Potapov, E. M. Semenov, V. P. Trofimov, N. N. Udodenko
Translated by H. H. McFADEN