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Creators/Authors contains: "Müller, J. Steffen"

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  1. ; ; (, Research in Number Theory)
    Free, publicly-accessible full text available March 1, 2026
  2. ; ; ; ; (, Compositio Mathematica)
    We describe how the quadratic Chabauty method may be applied to determine the set of rational points on modular curves of genus$$g>1$$whose Jacobians have Mordell–Weil rank$$g$$. This extends our previous work on the split Cartan curve of level 13 and allows us to consider modular curves that may have few known rational points or non-trivial local height contributions at primes of bad reduction. We illustrate our algorithms with a number of examples where we determine the set of rational points on several modular curves of genus 2 and 3: this includes Atkin–Lehner quotients$$X_0^+(N)$$of prime level$$N$$, the curve$$X_{S_4}(13)$$, as well as a few other curves relevant to Mazur's Program B. We also compute the set of rational points on the genus 6 non-split Cartan modular curve$$X_{\scriptstyle \mathrm { ns}} ^+ (17)$$. 
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  3. ; ; ; (, Israel Journal of Mathematics)
    null (Ed.)
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  4. ; ; ; ; (, Annals of mathematics)
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