Computational aspects of the diophantine problems

Project Information

Grant agreement ID: FMBI960848

Project closed

Start date 2 September 1996

End date 1 September 1998

Funded under

• Specific research and technological development programme in the field of the training and mobility of researchers, 1994-1998

Total cost No data

EU contribution No data

Coordinated by

Universität des Saarlandes
Germany

Objective

In my thesis, I have studied several diophantine problems and conjectur of Number Theory. In particular, the computational aspect of the abc and the Szpiro conjectures and their applications were extensively explored. I presented several algorithms to test these conjectures leading to the best examples currently known.
In future, I propose to continue to study some conjectures and diophantine problems in Number Theory. I wish to go deeper into four of them:
1. The abc conjecture for number fields. I wish to make explicit several parameters for it.
2. Links between minimal discriminant and conductor of hyperelliptic curves. The Szpiro's conjecture was extended to hyperelliptic curves by P. Lockhart. It remains to specify some parameters in this conjecture and to study its consequences.
3. Finding algebraic curves with several rational points.
4. Studying diophantine problems in number fields.
This work can be done using the computer algebra system SIMATH, develop by the research group of Prof. H.G. Zimmer at the university of Saarbruecken.

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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.

• natural sciences › mathematics › pure mathematics › arithmetics
• natural sciences › mathematics › pure mathematics › algebra

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Programme(s)

• FP4-TMR - Specific research and technological development programme in the field of the training and mobility of researchers, 1994-1998

Topic(s)

• 0302 - Post-doctoral research training grants
• TM21 - Algebra and Number Theory

Call for proposal

Data not available

Funding Scheme

RGI - Research grants (individual fellowships)

Coordinator

Universität des Saarlandes

• EU contribution: No data
• Address: 15,Im Stadtwald 15 ; 66041 Saarbrücken ; Germany
• Total cost: No data

Participants (1)

Not available

France

• EU contribution: No data
• Total cost: No data