Harder's conjecture for Picard modular forms
Harder's conjecture for Picard modular forms
Let and be in the critical range for the algebraic Hecke character , and define
Suppose a prime divides the denominator of . Harder's conjecture. There should exist a Picard modular cusp-form Hecke eigenform of weight
whose Hecke eigenvalues , for primes , satisfy
This predicts congruences between Picard modular forms and critical-value denominators in the spirit of Harder's conjectures.
Sources & referencesView supporting material
Primary source
Jonas Bergström and Gerard van der Geer, “Picard modular forms and the cohomology of local systems on a Picard modular surface”, arXiv:2012.07673 (2020).
Additional references
6 papers in this index state this conjecture (2006–2020). The statement above is taken from the most recent of them; the others are arXiv:1605.03450, arXiv:1603.07088, arXiv:1409.6090, arXiv:1203.5611, arXiv:math/0605346.
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