Zeros of families of automorphic $L$-functions close to 1

By Emmanuel Kowalski, P. Michel. 2002

67 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/194823adbdb9fe426a5882d214bf45acea206a3d

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In Algebra and Number Theory

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Citations in the corpus

An effective Chebotarev density theorem for families of number fields, with an application to $$\ell $$-torsion in class groups (2017, methodology): “1] and other works) have also applied [KM02] to certain families of isobaric representations, say π = π1 · · · πr of GL(m)/Q, with m = m1 + · · · + mr, and each πj a cuspidal automorphic representation of GL(mj)/Q.”
On the complex moments of symmetric power $L$-functions at $s = 1$ (2004, methodology): “Remark 11. We would like to point out that the multiplicity one result for symmetric powers, Corollary 5.2, is important in establishing the zero density result above and the Corollary 5.4: this is tied in with the duality method used in the proof of the large sieve inequality leading to Theorem 2 o”
Weak subconvexity without a Ramanujan hypothesis (2018, methodology): “107 m3 1 3 2(1−σ). Apart from the exponent, this corollary gives a general result which in special situations (or with additional hypotheses) was given by a number of authors; see Kowalski and Michel [18], Motohashi [24], Akbary and Trudgian [1], and Lemke Oliver and Thorner [19]. As a consequence o”
Upper bounds on L-functions at the edge of the critical strip (2009, background): “inally, we mention here that this convexity bound for L(s,π1 × π2) has several interesting and immediate applications. Brumley describes an extension of the zero density result of Kowalski and Michel [14] to all cusp forms on GL(n) over Qto n ≤ 4 based on his work in [2] which we can now extend to a”