# Constants for Artin like problems in Kummer and division fields

@inproceedings{Akbary2022ConstantsFA, title={Constants for Artin like problems in Kummer and division fields}, author={Amir Akbary and Milad Fakhari}, year={2022} }

A BSTRACT . We apply the character sums method of Lenstra, Moree, and Stevenhagen, to explicitly compute the constants in the Titchmarsh divisor problem for Kummer ﬁelds and for division ﬁelds of Serre curves. We derive our results as special cases of a general result on the product expressions for the sums in the form 8 ÿ in which g p n q is a multiplicative arithmetic function and t G p n qu is a certain family of Galois groups. Our results extend the application of the character sums method…

## References

SHOWING 1-10 OF 15 REFERENCES

### Character sums for primitive root densities

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 2014

Abstract It follows from the work of Artin and Hooley that, under assumption of the generalised Riemann hypothesis, the density of the set of primes q for which a given non-zero rational number r is…

### A GEOMETRIC VARIANT OF TITCHMARSH DIVISOR PROBLEM

- Mathematics
- 2012

We formulate a geometric analog of the Titchmarsh divisor problem in the context of abelian varieties. For any abelian variety A defined over ℚ, we study the asymptotic distribution of the primes of…

### A PROBLEM OF FOMENKO'S RELATED TO ARTIN'S CONJECTURE

- Mathematics
- 2012

Let a be a natural number greater than 1. For each prime p, let ia(p) denote the index of the group generated by a in . Assuming the generalized Riemann hypothesis and Conjecture A of Hooley, Fomenko…

### Analytic problems for elliptic curves

- Mathematics
- 2005

We consider some problems of analytic number theory for elliptic curves which can be considered as analogues of classical questions around the distribution of primes in arithmetic progressions to…

### On Artin's conjecture.

- Mathematics
- 1967

The problem of determining the prime numbers p for which a given number a is a primitive root, modulo JP, is mentioned, for the partieular case a — 10, by Gauss in the section of the Disquisitiones…

### Introduction to Elliptic Curves and Modular Forms

- Mathematics
- 1984

The theory of elliptic curves and modular forms provides a fruitful meeting ground for such diverse areas as number theory, complex analysis, algebraic geometry, and representation theory. This book…

### Primes of the Form x2 + ny2: Fermat, Class Field Theory, and Complex Multiplication

- Mathematics
- 1989

FROM FERMAT TO GAUSS. Fermat, Euler and Quadratic Reciprocity. Lagrange, Legendre and Quadratic Forms. Gauss, Composition and Genera. Cubic and Biquadratic Reciprocity. CLASS FIELD THEORY. The…

### A Course in Arithmetic

- Mathematics
- 1973

Part 1 Algebraic methods: finite fields p-adic fields Hilbert symbol quadratic forms over Qp, and over Q integral quadratic forms with discriminant +-1. Part 2 Analytic methods: the theorem on…

### Constants in Titchmarsh divisor problems for elliptic curves

- Mathematics, Computer ScienceResearch in Number Theory
- 2019

A comprehensive study of the constants C(E) emerging in the asymptotic study of these elliptic curve divisor sums in place of the constant C above is presented.