Roots of L-functions of characters over function fields, generic linear independence and biases
نویسندگان
چکیده
منابع مشابه
p-adic unit roots of L-functions over finite fields
In this brief note, we consider p-adic unit roots or poles of L-functions of exponential sums defined over finite fields. In particular, we look at the number of unit roots or poles, and a congruence relation on the units. This raises a question in arithmetic mirror symmetry.
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Let K/F be a quadratic extension of p-adic fields, and n a positive integer. A smooth irreducible representation of the group GL(n, K) is said to be distinguished, if it admits on its space a nonzero GL(n, F )-invariant linear form. In the present work, we classify distinguished generic representations of the group GL(n, K) in terms of inducing quasi-square-integrable representations. This has ...
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Example 1.1. A field homomorphism K → F is a character by restricting it to the nonzero elements of K (that is, using G = K×) and ignoring the additive aspect of a field homomorphism. In particular, when L/K is a field extension any element of Aut(L/K) is a field homomorphism L→ L and therefore is a character of L× with values in L×. Example 1.2. For any α ∈ F×, the map Z→ F× by k 7→ αk is a ch...
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Random matrix theory has successfully modeled many systems in physics and mathematics, and often analysis in one area guides development in the other. Hughes and Rudnick computed 1-level density statistics for low-lying zeros of the family of primitive Dirichlet L-functions of fixed prime conductor Q, as Q→∞, and verified the unitary symmetry predicted by random matrix theory. We compute 1and 2...
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Let K be a function field of odd characteristic, and let π (resp., η) be a cuspidal automorphic representation of GL2(AK ) (resp., GL1(AK )). Then we show that a weighted sum of the twists of L(s, π) by quadratic characters χD , ∑ D L(s, π ⊗ χD) a0(s, π, D) η(D) |D|, is a rational function and has a finite, nonabelian group of functional equations. A similar construction in the noncuspidal case...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2020
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2020.14.1291