Skip to main content
MathOverflow

Return to Question

edited title
Link
David Loeffler
David Loeffler
  • 37k
  • 3
  • 89
  • 194

The effect of base change on the L-function ogof GL(2)?

edited title
Link
Noah Schweber
Noah Schweber
  • 21.1k
  • 10
  • 110
  • 331

The affectioneffect of base change on the L-function og GL(2)?

Source Link
Monty
Monty
  • 1.8k
  • 9
  • 9

The affection of base change on the L-function og GL(2)?

Let $F$ be a local field (whose residue field is $q$) and $E$ its quadratic extension. Let $\pi$ be a irreducible principal series representation $\pi(\chi_1, \chi_2)$ of $GL_F(2)$ especially where $\chi_1, \chi_2$ are unitary characters. Then I know $L_F(s,\pi)=\frac{1}{1-\chi_1(\varpi)q^s} \cdot \frac{1}{1-\chi_2(\varpi)q^s}$. Then what is $L_E(s,BC(\pi))$ in terms of $\chi_1, \chi_2$?