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Automorphic symbols, p -adic L -functions and ordinary cohomology of Hilbert modular varieties
American Journal of Mathematics, 2013We introduce the notion of automorphic symbol generalizing the classical modular symbol and use it to attach very general $p$-adic $L$-functions to nearly ordinary Hilbert automorphic forms. Then we establish an exact control theorem for the $p$-adically completed cohomology of a Hilbert modular variety localized at a suitable nearly ordinary maximal ...
Mladen Dimitrov
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Automorphic functions on the upper half plane, especially modular functions
Lecture Notes in Mathematics, 1968Goro Shimura, Shimura Goro
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Analytic ranks of automorphic L$L$ ‐functions and Landau–Siegel zeros
Journal of the London Mathematical Society, 2023We relate the study of Landau–Siegel zeros to the ranks of Jacobians J0(q)$J_0(q)$ of modular curves for large primes q$q$ . By a conjecture of Brumer–Murty, the rank should be equal to half of the dimension.
Hung M. Bui, Kyle Pratt, A. Zaharescu
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