Objective
Content of the project.
The abc conjecture gives an upper bound for the logarithm of the largest absolute value of three nonvanishing integers with vanishing sum in terms of the logarithm of the product of their different prime factors, a quantity known as the radical. At the moment a bound of this type is known, but it is much weaker than the bound of the abc conjecture.
In the project the conjectured bound is replaced by a stronger bound, which reveals the structure of the abc conjecture. In fact, comparison with an analogous theorem in the field of meromorphic functions shows that the bound can be interpreted as a contribution to the radical itself. The plausibility of the stronger bound is based on a heuristic argument in the thesis of the applicant.
Objectives of the project.
The project aims to extend the heuristics to arbitrary number fields. Conversely, research will be carried out to prove that the proposed bound is the best possible. This will be an improvement of an already existing theorem.
The interpretation of the bound as a contribution to the radical suggests a connection with Riemann's Conjecture. In the project this connection will be investigated.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics arithmetics logarithmic functions
- natural sciences computer and information sciences artificial intelligence heuristic programming
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Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
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Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
91440 BURES-SUR-YVETTE
France
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.