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Before asking my short question I had made some research. Unfortunately I did not find a good reference with some examples. My question is the following What are the consequences of the Birch and ...

"The symmetric power $L$-functions are a powerful tool for studying algebraic or geometric objects through analytic methods." I read this sentence in the introduction of a Master thesis. I want to ...

$w=z=x+ 1 =y−1$ provides $wz−xy=w^2−(w−1)(w+ 1) = 1$. Hence if $x,y$ are odd then $w,z$ are even and all four integers are close. Is there elementary example where only $w$ is even and all four ...