STNB2024(37a edició)
Algorithms to compute Stark Numbers
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Carlos Caralps
Resum
In the 1970s, Harold Stark realized that the first coefficients of the Taylor expansions of some Zeta Functions at s=0 were related to integers in ray class fields, the Stark Numbers. The Stark Conjectures state that this property will be satisfied by all L functions. Since little is known about these coefficients for the Archimedean norm, we are interested in developing algorithms to compute Stark Numbers. The main aim of this presentation is to introduce methods to compute Stark Numbers, especially a new algorithm, developed together with Professeur Hugo Chapdelaine, that uses Eisenstein Series and a trick proposed by Professeur Pierre Colmez.
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