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SUMMARY:Peng-Jie Wong (University of Lethbridge)
DTSTART:20200605T020000Z
DTEND:20200605T023000Z
DTSTAMP:20260421T125803Z
UID:NTOC2020/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NTOC2020/12/
 ">Refinements of Strong Multiplicity One for GL(2)</a>\nby Peng-Jie Wong (
 University of Lethbridge) as part of Number Theory Online Conference 2020\
 n\n\nAbstract\nLet $f_1$ and $f_2$ be holomorphic newforms of same weight 
 and with same nebentypus\, and let  $a_{f_1}(n)$ and $a_{f_2}(n)$ denote t
 he Fourier coefficients of $f_1$ and $f_2$\, respectively. By the strong m
 ultiplicity one theorem\, it is known that if $a_{f_1}(p)=a_{f_2}(p)$ for 
 almost all primes $p$\, then  $f_1$ and $f_2$ are equivalent. Furthermore\
 , a result of Ramakrishnan states that if $a_{f_1}(p)^2=a_{f_2}(p)^2$ outs
 ide a set of primes $p$ of density less than $\\frac{1}{18}$\, then $f_1$ 
 and $f_2$ are twist-equivalent.\n\nIn this talk\, we will discuss some ref
 inements and variants of the strong multiplicity one theorem and Ramakrish
 nan's result for general $\\rm{GL}(2)$-forms. In particular\, we will anal
 yse the set of primes $p$ for which $|a_{f_1}(p)| \\neq |a_{f_2}(p)|$ for 
 non-twist-equivalent $f_1$ and $f_2$.\n
LOCATION:https://researchseminars.org/talk/NTOC2020/12/
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