## On the Zeros of a Class of Dirichlet Series |

### From inside the book

Results 1-3 of 14

Page 10

Proofs of theorems 1–3. Lemma I. Let a function p(s) represent in some half-

plane the Dirichlet series X, a, n °. Suppose that p(s) is regular and of finite order

in a half-plane a > , where s, is a

its ...

Proofs of theorems 1–3. Lemma I. Let a function p(s) represent in some half-

plane the Dirichlet series X, a, n °. Suppose that p(s) is regular and of finite order

in a half-plane a > , where s, is a

**positive constant**. Then, if Re z > 0 and zoo hasits ...

Page 36

Potter also investigated, for the class of integral (A, x, Y)functions, the behaviour

of the mean value M(a,T) for a = } x. He found that, in the case 0 < x < 2, [3,3] M(\x,

T) o 3 log T as T -- co, where 3 is some

Potter also investigated, for the class of integral (A, x, Y)functions, the behaviour

of the mean value M(a,T) for a = } x. He found that, in the case 0 < x < 2, [3,3] M(\x,

T) o 3 log T as T -- co, where 3 is some

**positive constant**(see Potter [2]).Page 45

with some constant A, not depending on 8 and o. Hence so |G (a, t) * dt - 21: A,

ST" (h 3 a s au). ... has no zeros in the rectangle h is a -s a 1, - a s t < a. Hence

there exists a

rectangle.

with some constant A, not depending on 8 and o. Hence so |G (a, t) * dt - 21: A,

ST" (h 3 a s au). ... has no zeros in the rectangle h is a -s a 1, - a s t < a. Hence

there exists a

**positive constant**b, such that |T(s) > b for s belonging to thisrectangle.

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### Contents

Introduction | 1 |

The number of zeros in a horizontal strip | 22 |

Some mean value theorems | 35 |

Copyright | |

2 other sections not shown

### Common terms and phrases

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