On mod p nonvanishing of special values of L-functions associated with cusp forms on GL2 over imaginary quadratic fields

Research output: Contribution to journalReview article

Abstract

Let f be a cusp formonGL2 over an imaginary quadratic field F of class number 1, and let p be an odd prime which satisfies some mild conditions. Then we show the existence of a finite-order Hecke character of F×A such that the algebraic part of the special value of L-functions of f at s=1 is a p-adic unit. This is an analogous result to the result of A. Ash and G. Stevens for GL2 over the field of rationals obtained in [AS].

Original languageEnglish
Pages (from-to)117-140
Number of pages24
JournalKyoto Journal of Mathematics
Volume52
Issue number1
DOIs
Publication statusPublished - Mar 1 2012
Externally publishedYes

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Imaginary Quadratic Field
Cusp Form
L-function
Class number
Fatty Acids
Cusp
P-adic
Odd
Unit
Character

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "Let f be a cusp formonGL2 over an imaginary quadratic field F of class number 1, and let p be an odd prime which satisfies some mild conditions. Then we show the existence of a finite-order Hecke character of F×A such that the algebraic part of the special value of L-functions of f at s=1 is a p-adic unit. This is an analogous result to the result of A. Ash and G. Stevens for GL2 over the field of rationals obtained in [AS].",
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N2 - Let f be a cusp formonGL2 over an imaginary quadratic field F of class number 1, and let p be an odd prime which satisfies some mild conditions. Then we show the existence of a finite-order Hecke character of F×A such that the algebraic part of the special value of L-functions of f at s=1 is a p-adic unit. This is an analogous result to the result of A. Ash and G. Stevens for GL2 over the field of rationals obtained in [AS].

AB - Let f be a cusp formonGL2 over an imaginary quadratic field F of class number 1, and let p be an odd prime which satisfies some mild conditions. Then we show the existence of a finite-order Hecke character of F×A such that the algebraic part of the special value of L-functions of f at s=1 is a p-adic unit. This is an analogous result to the result of A. Ash and G. Stevens for GL2 over the field of rationals obtained in [AS].

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