The Selberg trace formula for 𝑆𝐿(3,𝑍)\𝑆𝐿(3,𝑅)/𝑆𝑂(3,𝑅)

Dorothy Wallace

Type: Article

Publication Date: 1994-01-01

Citations: 4

DOI: https://doi.org/10.1090/s0002-9947-1994-1184117-4

Abstract

In this paper we compute the trace formula for <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S upper L left-parenthesis 3 comma double-struck upper Z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mi>L</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">Z</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">SL(3,\mathbb {Z})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in detail and refine it to a greater extent than has previously been done. We show that massive cancellation occurs in the parabolic terms, leading to a far simpler formula than had been thought possible.

Locations

Transactions of the American Mathematical Society - View - PDF

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