On the second moment for primes in an arithmetic progression
نویسندگان
چکیده
منابع مشابه
On the Second Moment for Primes in an Arithmetic Progression
Abstract. Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a constant factor of the conjectured asymptotic result for the second moment for primes in an individual arithmetic progression in short intervals. Previous results were averaged over all progression of a given modulus. The method uses a short divisor sum approximation for the von Mangoldt function, together w...
متن کاملPrimes in arithmetic progression
Prime numbers have fascinated people since ancient times. Since the last century, their study has acquired importance also on account of the crucial role played by them in cryptography and other related areas. One of the problems about primes which has intrigued mathematicians is whether it is possible to have long strings of primes with the successive primes differing by a fixed number, namely...
متن کاملNotes on Primes in Arithmetic Progression
The following is a quick set of notes of some properties of Dirichlet characters, in particular, how they are used to prove the infinitude of primes in arithmetic progressions. These notes are from from An Invitation to Modern Number Theory, by myself and Ramin Takloo-Bighash. As this is a modified snippet from the book, references to other parts of the book are displayed as ??. 1. Dirichlet Ch...
متن کاملDirichlet’s Theorem on Primes in an Arithmetic Progression
Our goal is to prove the following theorem: Dirichlet’s Theorem: For any coprime a, b ∈ Z, there are infinitely many primes p such that p ≡ a (mod b). Although the statement of the theorem involves only integers, the simplest proof requires the use of complex numbers and Dirichlet L-series. Most of this paper will therefore be devoted to proving some basic properties of characters and L-series,...
متن کاملArithmetic Progression Hypergraphs: Examining the Second Moment Method
In many data structure settings, it has been shown that using “double hashing” in place of standard hashing, by which we mean choosing multiple hash values according to an arithmetic progression instead of choosing each hash value independently, has asymptotically negligible difference in performance. We attempt to extend these ideas beyond data structure settings by considering how threshold a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2001
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa100-1-8