19 INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009 REMARKS ON THE PÓLYA – VINOGRADOV INEQUALITY
نویسنده
چکیده
We establish a numerically explicit version of the Pólya–Vinogradov inequality for the sum of values of a Dirichlet character on an interval. While the technique of proof is essentially that of Landau from 1918, the result we obtain has better constants than in other numerically explicit versions that have been found more recently. – Dedicated to Mel Nathanson on his 65th birthday
منابع مشابه
Remarks on the Pólya–Vinogradov inequality
Abstract: We establish a numerically explicit version of the Pólya– Vinogradov inequality for the sum of values of a Dirichlet character on an interval. While the technique of proof is essentially that of Landau from 1918, the result we obtain has better constants than in other numerically explicit versions that have been found more recently.
متن کاملINTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009 RECURSIVELY SELF - CONJUGATE PARTITIONS
A class of partitions that exhibit substantial symmetry, called recursively selfconjugate partitions, are defined and analyzed. They are found to have connections to non-squashing partitions and other combinatorial objects.
متن کامل9 INTEGERS 11 A ( 2011 ) Proceedings of Integers Conference 2009
We study the question of whether for each n there is an m �= n with λ(m) = λ(n), where λ is Carmichael’s function. We give a “near” proof of the fact that this is the case unconditionally, and a complete conditional proof under the Extended Riemann Hypothesis. –To Professor Carl Pomerance on his 65th birthday
متن کاملThe Smoothed Pólya–Vinogradov Inequality
Let χ be a primitive Dirichlet character to the modulus q. Let Sχ(M,N) = ∑ M<n≤N χ(n). The Pólya-Vinogradov inequality states that |Sχ(M,N)| √ q log q. The smoothed Pólya–Vinogradov inequality, recently introduced by Levin, Pomerance and Soundararajan, is a numerically useful version of the Pólya–Vinogradov inequality that saves a log q factor. The smoothed Pólya–Vinogradov inequality has been ...
متن کاملTHUE-VINOGRADOV AND INTEGERS OF THE FORM x +Dy
Introduction – Study of an Elementary Proof 1 1. The Lemmas of Thue and Vinogradov 4 2. Preliminaries on Quadratic Reciprocity and Quadratic Forms 4 2.1. Quadratic reciprocity law 4 2.2. Binary quadratic forms 5 3. Thue-Vinogradov Applied to Binary Quadratic Forms 7 4. First Applications of Theorem 9 8 4.1. Indefinite forms 8 4.2. Positive definite forms 10 5. Primes of the form x +Dy for idone...
متن کامل