# The Least Number with Prescribed Legendre Symbols

@article{Hanson2016TheLN, title={The Least Number with Prescribed Legendre Symbols}, author={Brandon Hanson and R. C. Vaughan and Ruixiang Zhang}, journal={arXiv: Number Theory}, year={2016} }

In this article we estimate the number of integers up to $X$ which can be represented by a positive-definite, binary integral quadratic form of discriminant which is small relative to $X$. This follows from understanding the vector of signs when computing the Legendre symbol of small integers $n$ at multiple primes.

#### References

SHOWING 1-7 OF 7 REFERENCES

Analytic Number Theory

- Mathematics
- 2004

Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large… Expand

A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations

- Mathematics
- 2000

and the (weaker) conjecture n q for all ε > 0 is known as Vinogradov’s conjecture. Linnik’s technique makes it possible to prove that the number of exceptions to these conjectures is extremely small.… Expand

The average least quadratic nonresidue modulo m and other variations on a theme of Erdős

- Mathematics
- 2012

Abstract For each m ⩾ 3 , let n 2 ( m ) denote the least quadratic nonresidue modulo m. In 1961, Erdős determined the mean value of n 2 ( p ) , as p runs over the odd primes. We show that the mean… Expand

Opera De Cribro

- Computer Science
- 2010

A wide range of applications are included, both to traditional questions such as those concerning primes, and to areas previously unexplored by sieve methods, such as elliptic curves, points on cubic surfaces and quantum ergodicity. Expand

Springer-Verlag

- New York,
- 1989

Chowla, On numbers which can be expressed as a sum of two squares

- Proc. Nat. Inst. Sci. India
- 1947