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1 results

  • Orbital $L$-functions for the Space of Binary Cubic Forms

  • Takashi Taniguchi, Frank Thorne
  • Journal:
    Canadian Journal of Mathematics / Volume 65 / Issue 6 / 01 December 2013
    Published online by Cambridge University Press:
    20 November 2018, pp. 1320-1383
    Print publication:
    01 December 2013
    • Article
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  • We introduce the notion of orbital $L$-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from their intrinsic interest, the results from this paper are used to prove the existence of secondary terms in counting functions for cubic fields. This is worked out in a companion paper.