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Langlands in his 1978 ICM talk made a conjecture that all motivic $L$-functions should arise as automorphic $L$-functions. A part of this conjecture, namely for some Hasse-Weil $\zeta$ functions is a ...

Hi, Given an algebraic Hecke character $\chi$ of a number field $k$ there should be a "rank 1 CM-motive" $M$ with $\overline Q$-coefficients such that $L(s,M) = L(s,\chi)$. This follows from the ...

Background: Today the notion of automorphic geometry is often framed in the context of the Langlands program, in particular what is sometimes called the Langlands reciprocity conjecture. This is ...

Background: There are several known lifts from integral weight modular forms to Siegel forms of genus 2, among them the Saito-Kurokawa lift. Another lift construction that is important for ...

Background: One prominent part of the Langlands program is the conjecture that all motives are automorphic. It is of interest to consider special cases that are more precise, if less sweeping. ...