scholarly journals Multiplicative structure of values of the Euler function

2004 ◽  
pp. 29-47 ◽  
Author(s):  
William Banks ◽  
John Friedlander ◽  
Carl Pomerance ◽  
Igor Shparlinski
Keyword(s):  
Multiplicative Structure ◽  
Euler Function

On the sum of the first n values of the Euler function

2014 ◽  
Vol 163 (3) ◽  
pp. 199-201 ◽  
Author(s):  
R. Balasubramanian ◽  
Florian Luca ◽  
Dimbinaina Ralaivaosaona
Keyword(s):  
Euler Function

Carmichael Numbers with a Square Totient

2009 ◽  
Vol 52 (1) ◽  
pp. 3-8 ◽  
Author(s):  
W. D. Banks
Keyword(s):  
Euler Function ◽  
Carmichael Numbers

AbstractLet φ denote the Euler function. In this paper, we show that for all large x there are more than x0.33 Carmichael numbers n ⩽ x with the property that φ(n) is a perfect square. We also obtain similar results for higher powers.

On the distribution in short intervals of products of a prime and integers from a given set

1998 ◽  
Vol 124 (1) ◽  
pp. 1-14
Author(s):  
J. KACZOROWSKI ◽  
A. PERELLI
Keyword(s):  
Number Theory ◽  
Classical Problem ◽  
Analytic Number Theory ◽  
Multiplicative Structure ◽  
Short Intervals ◽  
Analytic Number ◽  
Almost Primes ◽  
Prime Factors

A classical problem in analytic number theory is the distribution in short intervals of integers with a prescribed multiplicative structure, such as primes, almost-primes, k-free numbers and others. Recently, partly due to applications to cryptology, much attention has been received by the problem of the distribution in short intervals of integers without large prime factors, see Lenstra–Pila–Pomerance [3] and section 5 of the excellent survey by Hildebrand–Tenenbaum [1].In this paper we deal with the distribution in short intervals of numbers representable as a product of a prime and integers from a given set [Sscr ], defined in terms of cardinality properties. Our results can be regarded as an extension of the above quoted results, and we will provide a comparison with such results by a specialization of the set [Sscr ].

scholarly journals COHOMOLOGY RING OF THE BRST OPERATOR ASSOCIATED TO THE SUM OF TWO PURE SPINORS

2013 ◽  
Vol 28 (23) ◽  
pp. 1350107 ◽  
Author(s):  
ANDREI MIKHAILOV ◽  
ALBERT SCHWARZ ◽  
RENJUN XU
Keyword(s):  
Cohomology Ring ◽  
Type Ii ◽  
Pure Spinor ◽  
Multiplicative Structure ◽  
Dimensional Algebra ◽  
Dimensional Vector Space ◽  
Infinite Dimensional ◽  
Brst Operator ◽  
Finite Dimensional ◽  
Algebra Of Functions

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure.

On a sum involving the Euler function

2020 ◽  
Vol 211 ◽  
pp. 199-219 ◽  
Author(s):  
Wenguang Zhai
Keyword(s):  
Euler Function
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