اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn the Chowla and twin primes conjectures over $mathbb F_q[T]$
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Using geometric methods, we improve on the function field version of the Burgess bound, and show that, when restricted to certain special subspaces, the M{o}bius function over $mathbb F_q[T]$ can be mimicked by Dirichlet characters. Combining these, we obtain a level of distribution close to $1$ for the M{o}bius function in arithmetic progressions, and resolve Chowlas $k$-point correlation conjecture with large uniformity in the shifts. Using a function field variant of a result by Fouvry-Michel on exponential sums involving the M{o}bius function, we obtain a level of distribution beyond $1/2$ for irreducible polynomials, and establish the twin prime conjecture in a quantitative form. All these results hold for finite fields satisfying a simple condition.
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