DIOPHANTINE EQUATIONS OF THE FORM OVER FUNCTION FIELDS

DOI10.1017/s0004972723000412arXiv2207.03080OpenAlexW4377028142MaRDI QIDQ6090188

Anwesh Ray

Publication date: 14 November 2023

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.03080

zbMATH Keywords

Diophantine equations over function fieldsDiophantine equations involving power sums and arithmetic progressionspropagation of solutions in towers of function fields

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Higher degree equations; Fermat's equation (11D41)

Cites Work

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• On the Diophantine equation \((x+1)^2+(x+2)^2+\ldots+(x+d)^2=y^n\)
• On \(S\)-integral solutions of the equation \(y^ m=f(x)\)
• On the Diophantine equation \((x+1)^{k}+(x+2)^{k}+\ldots+(2x)^{k}=y^{n}\)
• On perfect powers that are sums of cubes of a seven term arithmetic progression
• On a conjecture of Schäffer concerning the equation \(1^k + \ldots + x^k = y^n\)
• Rational points of Abelian varieties with values in towers of number fields
• Rational points on algebraic curves in infinite towers of number fields
• PERFECT POWERS THAT ARE SUMS OF CONSECUTIVE CUBES
• Perfect powers that are sums of consecutive squares
• On the Diophantine equation $1^k+2^k+\dotsb+x^k=y^n$
• Perfect powers that are sums of squares in a three term arithmetic progression
• Le Veque's superelliptic equation over function fields
• On the equation $y^m=f(x)$
• Class Number in Constant Extensions of Elliptic Function Fields

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