SCIENTIFIC ABSTRACT VINOGRADOV, A.I. - VINOGRADOV, A.M.

• Document Type: CREST
• Collection: Scientific Abstracts
• Document Number (FOIA) /ESDN (CREST): CIA-RDP86-00513R001859910006-2
• Release Decision: RIF
• Original Classification: S
• Document Page Count: 100
• Document Creation Date: November 2, 2016
• Document Release Date: September 1, 2001
• Sequence Number: 6
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

VINOGRADOV, A.I.
7--- -,- - -
Generalization of Klostermann's for=Lla. DoU. AN SSSR
146 no.4:754,-756 0 162. (MMA 15sll)
1. Isningradekop otdoleniye Matematicheskogo instituta
im. V.A. Steklova AN SSSR. Predstavieno akademikom
I.M. Vinogradovym.
(Numbers,, Prime)

I I I ~ t . , , .1 . . :

VINOGRADGV,__Lj. (Ioningrad)
The sieve method in algebraic fields. Mat. sbDr. 64 no-1;
52-78 Yq 164. (MIRA 17:6)

V/ IV 6 V
MR/Maihematias - Theory of numbers
caw 1/1 Pub. 22 - 5/54
Authors. 1, Vinogradov,, A. 1.
Tit-Is - g On new theorems of.the additive theory of numbers
Perlodie4 t Dok. AN SSSR 102/5, 875-676, June 3-1., 1955
-Abstract s Theorems dealing with the addition of two prime numbers with "rare
sequences" am proved. The proof was accomplished in view of theorems
on zeros L(S,X) by Dirichlet, Linnik and others and the theorems on
evaluations of the trigonometric sums by Vinogradov. Ono USSR refer-
ence (1951)
institution i The Acad. of So.p JTSSR, V. A. Stoklov Institiito of liathinmutical
Sciences
Presented bys Academician I. M. Vinogradov, March 4. 1955
M, --M
~77 7

A
Call Nr: AF ilo8825
Transactions of the Third A12-union Mathematical Congress (Cont. )MOSCOV,
gun-Jul '56, Trudy 156 V. 1, Seat. Rpts., Izdatel'stvo An SSSR, Moscov, 1956 237 pp.
Vinogradov A. I. (Leningrad). New Additive Problems
4
Demlyanov, B. V. (Moscow). on Hypothesis Concerning the
Expression of Zero by Forms With p adie coefficients. 4-5
There are 2 references, both USSR.
Kogoniya, P. G. (Tbilisi). On the Set of Condensation Points
of Markov's Number Set. 5
There are 2 references, I USSR and I German.
Kubilyus, I. P. (VilInyus). On Distribution Values of
Theoretical Number Functions. 5-6
Mintion is made of Kolmogorov., A. N.
1
Levin, B. V. (Tashkent). On a Special Class of Differential
Operators Which is Connected With the Theory of Modular Functions
and the Theory of Numbers. 6
Card 3/80

A. I.
SiGws-mtbO4,-**TMUAi&"'Vittf-tbo Rieman' s-function. Vogt.
Lun. un; 11 no,13:142-146 !56. (MLRA 9:10)
(Functions. Zeta) (Aggregates)

SUBJECT USSR/MATHMATICS/Humber theory CARD 1/2 PG - 579
AUTHOR VINOGRLDOV Aj.
TITLE 04 an "almost binary" problem.
PERIODICAL Izvestija 1kad.ffauk 20, 713-750 (1956)
reviewed 2/1957
The author proves some additive theorems on prize numbers whicht in a certain
sense# form an approximation to the binary problem of Goldbach. The principal
result of the present paper is contained in the following theoromt For all
N> NO a k. can be determined such that every X7No can be represented in
the form N - Pl + P2 + Exipxi + xx2pX2 + *90 + ZXk pxk 0
Here p, and P2 are prime numbers, xi,--Nl k,,-r-kop xltx?-#*"Pxk all different
from eachother. The numbers N and p-k are both either even or odd.
Therefrom followas If a sufficiently large number N is written in the form
N - so + alp + *.* + aRpR
and if the sun of two prime numbers is wanted, then it is sufficient to
change by + I a number of coefficients bounded by an absolute constant,
where the zeros are replaced by +1 and the number p-l is replaced by -1.

Izvestija Akad. Hauk 20. 713-750 0956) CARD 2/2 PG - 579
The proof is given according to the method of Linnik (Mat. Sbornik, n. Ser.
3-2-L 3-60 (1953)).
An improved assertion can be obtained under the assumption of the extended
Riemannian conjecture.
I
-A
INSTITUTIONs W%th. Ins t. load. Sci. fZ~

SUBJECT USSR/VATMUTICS/Number theory CARD 1/2 PG - 338
AUTHOR VINOGRADOV A. I.
TITLE small prime divisors.
PERIODICAL Doklady Akad, Nauk 109. 683-686 (1956)
reviewed 1011956
In extension of the well-known results on nil-bore the prime divisors of which
have an upper bound, the author proves the following theoremss
it Lot F(xpz#q) be the number of integers:5x which are relatively prime with
q Ax and the prime divisors of which are * z.
a) if in then
1P(x,z,q)O.
Some further similar assertions relat-,.ng partly to the fun-to~,,n~t
of A.A. BukhsktabLf7Ref 2-7are given. An arithmetically
evaluable imp_rovemez-~ of the well-known estimation--. is not
reached.
There are 2 Soviet references.
SUBMITTEDt October 10, 1957
Card 2/2

16(1)
AUTHOR. Vinog'r SOV/43-59-19-6/14
TITLE& On an Estimation of Quadratic Forms Used in Arithmetic.,
PERIODICAL., Vestnik Laningradskogo universiteta, Seriya matematiki,
m9khaniki i astronomli, 1959, Nr 19M, pp 60-63 (USSR)
APSTRACT: Let P,A,B,C,D - B2 + 4kC be integers, where exists a number N and
a constant tA>O for which IDIN't Let D - D D, 2, whGre
D 1 is free of squares; for an integral y let
VW - F1 (1+ 2 10
P/y
Theorem: It holds
P r4(C + Bx - Ax2)X so that coker fp - 0, ker fp a K (X). The
p p A W
space X with these properties is determined uniquely up to the singular
p
homotopic type (i.e. the spaces have the same singular homotopic type VI\
if their natural systems are isomorpbic).
Definition 1t The space X is called a p-epace if it has the same
honotopic type as ihs.spice Xp.
Lemma 2s Adams sequences with reapect to mod p, calculated for X and Xp
are isomorphic and this isomorphism is realized by 4 -
Definition 21 A p-system of a p-space X is a system of fiberings
F1 F2
(1) X0 X1 X2
Ti 32 93
which satisfies the following conditiones
1) The limit space 1 of this system has the same singular homotopic
type as X.
2) The/spaces Xo F19F21"' are direct products of spaces of the type
Card 2 4