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- W2896804555 abstract "Abstract In this paper, we study some shifted convolution sums for higher rank groups. In particular, we establish an asymptotic formula for a <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:mrow> <m:mi>GL</m:mi> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mn>4</m:mn> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mo>×</m:mo> <m:mi>GL</m:mi> </m:mrow> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mn>2</m:mn> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> {mathrm{GL}(4)timesmathrm{GL}(2)} shifted convolution sum <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:mrow> <m:munder> <m:mo>∑</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo>≤</m:mo> <m:mi>x</m:mi> </m:mrow> </m:munder> <m:mrow> <m:msup> <m:mrow> <m:mo>|</m:mo> <m:mrow> <m:msub> <m:mi>λ</m:mi> <m:mi>f</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>n</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> <m:mo>|</m:mo> </m:mrow> <m:mn>2</m:mn> </m:msup> <m:mo></m:mo> <m:msub> <m:mi>r</m:mi> <m:mi>l</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>n</m:mi> <m:mo>+</m:mo> <m:mi>b</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:mrow> <m:mo>,</m:mo> </m:mrow> </m:math> sum_{nleq x}lvertlambda_{f}(n)rvert^{2}r_{l}(n+b), where <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>λ</m:mi> <m:mi>f</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>n</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> {lambda_{f}(n)} are normalized Fourier coefficients of a Hecke holomorphic cusp form and <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>r</m:mi> <m:mi>l</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>n</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> {r_{l}(n)} denotes the number of representations of n by the quadratic form <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msubsup> <m:mi>x</m:mi> <m:mn>1</m:mn> <m:mn>2</m:mn> </m:msubsup> <m:mo>+</m:mo> <m:mi>⋯</m:mi> <m:mo>+</m:mo> <m:msubsup> <m:mi>x</m:mi> <m:mi>l</m:mi> <m:mn>2</m:mn> </m:msubsup> </m:mrow> </m:math> {x_{1}^{2}+cdots+x_{l}^{2}} ." @default.
- W2896804555 created "2018-10-26" @default.
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- W2896804555 date "2018-10-16" @default.
- W2896804555 modified "2023-10-15" @default.
- W2896804555 title "Shifted convolution sums for higher rank groups" @default.
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- W2896804555 doi "https://doi.org/10.1515/forum-2017-0269" @default.
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