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• W3021379779 abstract "Let $F$ be a number field and $D$ a quaternion algebra over $F$. Take a cuspidal automorphic representation $pi$ of $D_mathbb{A}^times$ with trivial central cahracter. We study the zeta functions with period integrals on $pi$ for the perhomogeneous vector space $(D^timestimes D^timestimesmathrm{GL}_2, Doplus D)$. We show their meromorphic continuation and functional equation, determine the location and orders of possible poles and compute the residue. Arguing along the theory of Saito and computing unramified local factors, the explicit formula of the zeta functions is obtained. Counting the order of possible poles of this explicit formula, we show that if $L(1/2, pi)neq0$, there are infinitely many quadratic extension $E$ of $F$ which embeds in $D$, such that $pi$ has nonvanishing toric period with respect to $E$." @default.
• W3021379779 created "2020-05-13" @default.
• W3021379779 creator A5051894776 @default.
• W3021379779 creator A5063126942 @default.
• W3021379779 date "2020-05-05" @default.
• W3021379779 modified "2023-09-27" @default.
• W3021379779 title "Zeta functions and nonvanishing theorems for toric periods on $mathrm{GL}_2$" @default.
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• W3021379779 hasPublicationYear "2020" @default.
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