An Alternate Argument for the Arithmetic Large Sieve Inequality
نویسنده
چکیده
the notation ∑[ and ∑∗ denoting, respectively, a sum over squarefree integers, and one over integers coprime with the (implicit) modulus, which is q here. By work of Montgomery-Vaughan and Selberg, it is known that one can take ∆ = Q − 1 +N (see, e.g., [IK, Th. 7.7]). There are a number of derivations of (1) from (2); for one of the earliest, see [M1, Ch. 3]. The most commonly used is probably the argument of Gallagher involving a “submultiplicative” property of some arithmetic function (see, e.g., [K, §II.2] for a very general version). We will show in this note how to prove (1) quite straightforwardly from the dual version of the harmonic large sieve inequality: ∆ is also any constant for which
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تاریخ انتشار 2008