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# 1. Introduction. If p is a prime, we define g

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(1)

r

ε

Oε(log3p)

1

n

n−1

Oε(log3p/ log4p)

r

r

ε,η

2

B

ε,η

ε

r

r

[277]

(2)

ε

44/5+ε

22/5

×q

E(q)/s(φ(q))

0

×q

2

1

−10

1/(1−σ)

σ

σ,θ

θ

−10

1

1

4

2

(3)

1

4

6

0

0

−1

θ

ε,η

ε

1/20

α(l)

l|E

lα(l)

m(l)

p

p

pα(p)

m(p)

l|E l6=p

lα(l)

m(l)

p

m(p)

(4)

d

d

p|d

p

m(d)

p|d

m(p)

m(d)

1

d

m(d)

p

p|E

p

p

d

d

d

E/d

s(E)

d

d

d

d

χ∈Φd

d

d

m(d)

0

×q

p

0

p|φ(q)

m(p)

−10

1

(5)

1

1

n<x

1

1+σ

1

2+i∞

2−i∞

0

s+1

1

%

%+1

1

β≤σ

1+β

2

|γ|≥T

1+β

2

|γ|≥T

−2

−1

1

1+σ

2

−1

a∈A (ν(a),Υ )=1

d

a∈A d|ν(a)

(6)

d

1

1

1

p|Υ

2

j

ω(Υ )

p≤z

d

1

n

d|n

d

n

p|Υ

d|P

d

p|d

d|P

d

1

2

d

d

1

r

1

r

d

r

1

2l−1

2l3

d

2

4

d|P

d

−2

d|P

d

p|d

γ

2

2

2

γ

γ

2

2

1

(7)

1

2

1

p|Υ

2

2

2

2

1

2

1

n<x

d

1

d

n<x d|ν(n)

n<x

d

d

χ∈Φd

n<x

m(d)

1

0

d

χ∈Φd

χ6=χ0

1

1

n<x

1

1

0

n<x (n,q)>1

p|q

r≥1 pr<x

d

m(d)

1

1+σ

1

m(d)

(8)

1+σ

1

1

1

0

1+σ

2

1

1

1

0

−1+σ

2

1

−10

1

1

1

0

−1

1−σ

1

2

r σ

r

σ

0

0

0

r

r

2

2

r

r

0

2

0

0

q<Y

χ (mod q)

q<Y

χ (mod q)

δ

2

6(1−σ)/(5σ−1)+δ

θ

−1

0

ε,η

ε

(9)

1

t

1

t

rii

2

r11

rtt

(q)

(q)

(nq)1

0

0

0

0

0

0

0

0

0

(nq)1

(nq)1

(n2 0)

(q30)

E(nq)/s(E(nq))

(n2 0)

(q30)

rii

0

0

r11−1

rtt−1

2

r11

rtt

2

r11

rtt

0

(n2 0)

(q30)

E(nq)/s(E(nq))

(n2 0)

E(nq)/s(E(nq))

(q00)

(q00)

0

(nq)1

(q)

0

0

(q)

3

log z

1−δ

(10)

δ

2

3

log z

i

rii−1

rii

t i=1

rii

2

r11

rtt

i

t i=1

rii

i

2

r11

rtt

2

t

i=1

i

2

t

3

log z

δ

3

1/2

3

1−δ

p<x p≡1 (mod d)

−1

2

δ

2

r11

rtt

2

r11

rtt

δ

## x(log x)

−1/φ(φ2(q)pr11 ...prtt )

2

r11

rtt

δ

2

3

log z

(11)

## (19) X

q<x q∈R(17/22,x1/20)

.997

## and X

x<q q∈R(17/22,x1/20)

−1

−.003

1/20

## X

q<x q∈R(17/22,x1/20)

41861/42000

q<Y q∈R(σ,T )

3

3

2

1/(2 log z)

4

3

4

q<log3Y

4

3

4

## Y )) + X

log3Y ≤q<Y q∈R(σ,T )

1/20

1/20

3

4

3

4

3

.003

## which establishes the lemma.

(12)

### Received on 21.10.1996 (3064)

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