Squarefree polynomials and möbius values in short intervals and arithmetic progressions
| Autor: | Jon P Keating, Zeév Rudnick |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Short intervals
squarefrees Context (language use) 0102 computer and information sciences Möbius function 01 natural sciences Equidistribution 11M38 equidistribution short intervals 11T55 Squarefrees Unitary group FOS: Mathematics Number Theory (math.NT) Limit (mathematics) 0101 mathematics Arithmetic Mathematics Ring (mathematics) Algebra and Number Theory Mathematics - Number Theory Chowla’s conjecture 010102 general mathematics 11M50 Square-free integer Algebraic number field function fields Finite field Chowla's conjecture 010201 computation theory & mathematics Good–Churchhouse conjecture Function fields |
| Zdroj: | Keating, J P & Rudnick, Z 2016, ' Squarefree polynomials and möbius values in short intervals and arithmetic progressions ', Algebra and Number Theory, vol. 10, no. 2, pp. 375-420 . https://doi.org/10.2140/ant.2016.10.375 Algebra Number Theory 10, no. 2 (2016), 375-420 |
| DOI: | 10.2140/ant.2016.10.375 |
| Popis: | We calculate the mean and variance of sums of the M\"obius function and the indicator function of the squarefrees, in both short intervals and arithmetic progressions, in the context of the ring of polynomials over a finite field of $q$ elements, in the limit $q\to \infty$. We do this by relating the sums in question to certain matrix integrals over the unitary group, using recent equidistribution results due to N. Katz, and then by evaluating these integrals. In many cases our results mirror what is either known or conjectured for the corresponding problems involving sums over the integers, which have a long history. In some cases there are subtle and surprising differences. The ranges over which our results hold is significantly greater than those established for the corresponding problems in the number field setting. Comment: Added references and corrected misprints |
| Databáze: | OpenAIRE |
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