# Multiplicative Number Theory

@inproceedings{Davenport1967MultiplicativeNT, title={Multiplicative Number Theory}, author={Harold Davenport}, year={1967} }

From the contents: Primes in Arithmetic Progression.- Gauss' Sum.- Cyclotomy.- Primes in Arithmetic Progression: The General Modulus.- Primitive Characters.- Dirichlet's Class Number Formula.- The Distribution of the Primes.- Riemann's Memoir.- The Functional Equation of the L Function.- Properties of the Gamma Function.- Integral Functions of Order 1.- The Infinite Products for xi(s) and xi(s,Zero-Free Region for zeta(s).- Zero-Free Regions for L(s, chi).- The Number N(T).- The Number N(T, chi…

## 2,272 Citations

### The simple zeros of the Riemann zeta-function

- Mathematics
- 2016

The Simple Zeros of the Riemann Zeta-Function by Melissa Miller There have been many tables of primes produced since antiquity. In 348 BC Plato studied the divisors of the number 5040. In 1202…

### LIMITING DISTRIBUTIONS AND ZEROS OF ARTIN L-FUNCTIONS

- Mathematics
- 2000

This thesis is concerned with behaviour of some famous arithmetic functions. The first part of the thesis deals with prime number races. Rubinstein-Sarnak [62] developed a technique to study primes…

### Small zeros of Dirichlet L-functions of quadratic characters of prime modulus

- Mathematics
- 2018

In this paper, we investigate the distribution of the imaginary parts of zeros near the real axis of Dirichlet $L$-functions associated to the quadratic characters $\chi_{p}(\cdot)=(\cdot |p)$ with…

### PRIME POLYNOMIALS IN SHORT INTERVALS AND IN ARITHMETIC PROGRESSIONS

- Mathematics
- 2015

In this paper we establish function field versions of two classical conjectures on prime numbers. The first says that the number of primes in intervals (x,x x(is an element of)] is about x(is an…

### Generalized divisor functions in arithmetic progressions: I The k-fold divisor function in arithmetic progressions to large moduli

- Mathematics
- 2021

We prove some distribution results for the k-fold divisor function in arithmetic progressions to moduli that exceed the square-root of length X of the sum, with appropriate constrains and averaging…

### On Elementary Proofs of the Prime Number Theorem for Arithmetic Progressions, without Characters

- Mathematics
- 1993

We consider what one can prove about the distribution of prime numbers in arithmetic progressions, using only Selberg's formula. In particular, for any given positive integer q, we prove that either…

### AN EXTENSION OF THE PAIR-CORRELATION CONJECTURE AND APPLICATIONS

- Mathematics
- 2016

Abstract. We study an extension of Montgomery’s pair-correlation conjecture and its rele-vance in some problems on the distribution of prime numbers.Keywords. Riemann zeta function, pair correlation…

### ON THE IDENTITIES BETWEEN THE ARITHMETIC FUNCTIONS

- Mathematics
- 2015

Abstract. Dirichlet series is a Riemann zeta function attachedwith an arithmetic function. Here, we studied the properties ofDirichlet series and found some identities between arithmetic func-tions.…

### Discrete Mean Values of Dirichlet L-functions

- Mathematics
- 2015

In 1911 Landau proved an asymptotic formula for sums of the form ∑ γ≤T x ρ over the imaginary parts of the nontrivial zeros of the Riemann zeta function. The formula provided yet another deep…

### A Bombieri-Vinogradov theorem for all number fields

- Mathematics
- 2012

The classical theorem of Bombieri and Vinogradov is generalized to a non-abelian, non-Galois setting. This leads to a prime number theorem of “mixed-type” for arithmetic progressions “twisted” by…