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2 results

  • On anticyclotomic μ-invariants of modular forms

  • Part of
  • Robert Pollack, Tom Weston
  • Journal:
    Compositio Mathematica / Volume 147 / Issue 5 / September 2011
    Published online by Cambridge University Press:
    27 July 2011, pp. 1353-1381
    Print publication:
    September 2011
    • Article
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  • We prove the μ-part of the main conjecture for modular forms along the anticyclotomic Zp-extension of a quadratic imaginary field. Our proof consists of first giving an explicit formula for the algebraic μ-invariant, and then using results of Ribet and Takahashi showing that our formula agrees with Vatsal’s formula for the analytic μ-invariant.

  • CONGRUENCES FOR THE COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS

  • STEPHANIE TRENEER
  • Journal:
    Proceedings of the London Mathematical Society / Volume 93 / Issue 2 / September 2006
    Published online by Cambridge University Press:
    07 August 2006, pp. 304-324
    Print publication:
    September 2006

  • Recent works have used the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. We show that this type of phenomenon is completely general, by finding similar congruences for the coefficients of any weakly holomorphic modular form on any congruence subgroup $\Gamma_0 (N)$. In particular, we give congruences for a wide class of partition functions and for traces of CM values of arbitrary modular functions on certain congruence subgroups of prime level.