Product of an integer free of small prime factors and prime in arithmetic progression
نویسندگان
چکیده
We establish estimates for the number of ways to represent any reduced residue class as a product prime and an integer free small factors. Our best results is conditional on Generalised Riemann hypothesis (GRH). As corollary, we make progress conjecture Erdös, Odlyzko, Sárközy.
منابع مشابه
Polynomial values free of large prime factors
For F ∈ Z[X], let ΨF (x, y) denote the number of positive integers n not exceeding x such that F (n) is free of prime factors > y. Our main purpose is to obtain lower bounds of the form ΨF (x, y) x for arbitrary F and for y equal to a suitable power of x. Our proofs rest on some results and methods of two articles by the third author concerning localization of divisors of polynomial values. Ana...
متن کاملIntegers Free of Large Prime Factors
Deene (x;y) to be the number of positive integers n x such that n has no prime divisor larger than y. We present a simple algorithm that approximates (x; y) in O(yf log log x log y + 1 log log y g) oating point operations. This algorithm is based directly on a theorem of Hildebrand and Tenenbaum. We also present data which indicate that this algorithm is more accurate in practice than other kno...
متن کاملinjective modules and prime ideals
محور اصلی این پایان نامه، r- مدولهای a – انژکتیو می باشد که آنها را به عنوان یک تعمیم از مدول های انژکتیو معرفی می کنیم. در ابتدا مدول های انژکتیو را معرفی کرده، سپس برخی نتایج مهم وشناخته شده مدول های انژکتیو را به مدول های a – انژکتیو تعمیم می دهیم. در ادامه رابطه بین مدول های a – انژکتیو و حلقه های نوتری را بررسی می کنیم. پس هدف کلی این پایان نامه این است که با بررسی انژکتیو بودن ایده آله...
15 صفحه اولOn generalisations of almost prime and weakly prime ideals
Let $R$ be a commutative ring with identity. A proper ideal $P$ of $R$ is a $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$, $a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$, for some $iin{1,ldots,n}$; ($m,ngeq 2$). In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-...
متن کاملdevelopment and implementation of an optimized control strategy for induction machine in an electric vehicle
in the area of automotive engineering there is a tendency to more electrification of power train. in this work control of an induction machine for the application of electric vehicle is investigated. through the changing operating point of the machine, adapting the rotor magnetization current seems to be useful to increase the machines efficiency. in the literature there are many approaches wh...
15 صفحه اولذخیره 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: Monatshefte für Mathematik
سال: 2021
ISSN: ['0026-9255', '1436-5081']
DOI: https://doi.org/10.1007/s00605-021-01606-9