Determination of a pair of newforms from the product of their twisted central values
Determination of a pair of newforms from the product of their twisted central values
Abstract We show that a pair of newforms <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>f</m:mi> <m:mo>,</m:mo> <m:mi>g</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:math> (f,g) can be uniquely determined by the product of the central 𝐿-values of their twists. To achieve our goal, we prove an asymptotic formula for the average of the product …