Theses

The first such conjecture -- commonly associated with Chowla -- asserts the equidistribution of the parity of the number of primes dividing the integers represented by a polynomial. We prove the conjecture for homogeneous polynomials of degree 3.

The second conjecture used states that any non-constant homogeneous polynomial yields to a square-free sieve. We sharpen the existing bounds on the known cases by a sieve refinement and a new approach combining height functions, sphere packings and sieve methods.

Cited literature [68 references]

https://tel.archives-ouvertes.fr/tel-00010129

Contributor : Harald Andres Helfgott <>

Submitted on : Wednesday, September 14, 2005 - 1:53:58 AM

Last modification on : Tuesday, October 15, 2019 - 1:13:46 AM

Long-term archiving on: : Friday, April 2, 2010 - 9:53:29 PM

Contributor : Harald Andres Helfgott <>

Submitted on : Wednesday, September 14, 2005 - 1:53:58 AM

Last modification on : Tuesday, October 15, 2019 - 1:13:46 AM

Long-term archiving on: : Friday, April 2, 2010 - 9:53:29 PM