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All Outputs (8)

Integrality of twisted L-values of elliptic curves (2022)
Journal Article
Wiersema, H., & Wuthrich, C. (2022). Integrality of twisted L-values of elliptic curves. Documenta Mathematica, 27, 2041-2066. https://doi.org/10.25537/dm.2022v27.2041-2066

Under suitable, fairly weak hypotheses on an elliptic curve E/Q and a primitive non-trivial Dirichlet character χ, we show that the algebraic L-value L (E, χ) at s = 1 is an algebraic integer. For instance, for semistable curves L (E, χ) is integral... Read More about Integrality of twisted L-values of elliptic curves.

Numerical modular symbols for elliptic curves (2017)
Journal Article
Wuthrich, C. (2018). Numerical modular symbols for elliptic curves. Mathematics of Computation, 87(313), 2393-2423. https://doi.org/10.1090/mcom/3274

We present a detailed analysis of how to implement the computation of modular symbols for a given elliptic curve by using numerical approximations. This method turns out to be more effcient than current implementations as the conductor of the curve i... Read More about Numerical modular symbols for elliptic curves.

A moduli interpretation for the non-split Cartan modular curve (2017)
Journal Article
Rebolledo, M., & Wuthrich, C. (2018). A moduli interpretation for the non-split Cartan modular curve. Glasgow Mathematical Journal, 60(2), https://doi.org/10.1017/S0017089517000180

Modular curves like X0(N) and X1(N) appear very frequently in arithmetic geometry. While their complex points are obtained as a quotient of the upper half plane by some subgroups of SL2(Z), they allow for a more arithmetic description as a solution t... Read More about A moduli interpretation for the non-split Cartan modular curve.

Vanishing of some Galois cohomology groups for elliptic curves (2016)
Book Chapter
Lawson, T., & Wuthrich, C. (2016). Vanishing of some Galois cohomology groups for elliptic curves. In D. Loeffler, & S. L. Zerbes (Eds.), Elliptic curves, modular forms and Iwasawa theory: in honour of John H. Coates' 70th birthday, Cambridge, UK, March 2015. Springer

Let E/Q be an elliptic curve and p be a prime number, and let G be the Galois group of the extension of Q obtained by adjoining the coordinates of the p-torsion points on E. We determine all cases when the Galois cohomology group H1(G;E[p] does not v... Read More about Vanishing of some Galois cohomology groups for elliptic curves.

On Mordell–Weil groups and congruences between derivatives of twisted Hasse–Weil L-functions (2015)
Journal Article
Burns, D., Macias Castillo, D., & Wuthrich, C. (2018). On Mordell–Weil groups and congruences between derivatives of twisted Hasse–Weil L-functions. Journal für die reine und angewandte Mathematik, 2018(734), 187-228. https://doi.org/10.1515/crelle-2014-0153

Let A be an abelian variety defined over a number field k and let F be a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F we compute explicitly the algebraic part of the p-component of... Read More about On Mordell–Weil groups and congruences between derivatives of twisted Hasse–Weil L-functions.

On the Galois structure of Selmer groups (2015)
Journal Article
Burns, D., Castillo, D. M., & Wuthrich, C. (2015). On the Galois structure of Selmer groups. International Mathematics Research Notices, 2015(22), 11909-11933. https://doi.org/10.1093/imrn/rnv045

© 2015 The Author(s). Let A be an abelian variety defined over a number field k and F a finite Galois extension of k. Let p be a prime number. Then under certain not-too-stringent conditions on A and F, we investigate the explicit Galois structure of... Read More about On the Galois structure of Selmer groups.