Frequencies of Successive Tuples of Frobenius Classes

Frequencies of Successive Tuples of Frobenius Classes

In this paper, we consider the sequence of Frobenius conjugacy classes for a Galois extension K/Q, ordered by the increasing sequence of rational primes. For a given K, we look at the frequencies of non-overlapping consecutive k-tuples in this sequence. We compare these frequencies to what would be expected by the Chebotarev Density Theorem, if there were statistical independence between succes...

the impact of attending efl classes on the level of depression of iranian female learners and their attributional complexity

می توان گفت واقعیت چند لایه ا ی کلاس های زبان انگلیسی بسیار حائز اهمیت است، زیرا عواطف و بینش های زبان آموزان تحت تاثیر قرار می گیرد. در پژوهش پیش رو، گفته می شود که دبیران با در پیش گرفتن رویکرد فرا-انسانگرایی ، قادرند در زندگی دانش آموزانشان نقش مهمی را ایفا سازند. بر اساس گفته ی ویلیامز و بردن (2000)، برای کرل راجرز، یکی از بنیان گذاران رویکرد انسانگرایی ، یادگیری بر مبنای تجربه، نوعی از یاد...

Probability of Mutually Commuting N-Tuples in Some Classes of Compact Groups

Frequencies of Successive Pairs of Prime Residues

We consider statistical properties of the sequence of ordered pairs obtained by taking the sequence of prime numbers and reducing modulo m. Using an inclusion/exclusion argument and a cut-off of an infinite product suggested by Pólya, we obtain a heuristic formula for the “probability” that a pair of consecutive prime numbers of size approximately x will be congruent to (a, a+d) modulo m. We de...

Frobenius Classes in Alternating Groups

We present a method, based on an old idea of Serre, for completely computing Frobenius classes in alternating groups. We contrast this method with other approaches in examples involving the alternating groups A3 and A9. The method can be useful for proper subgroups of alternating groups as well, and we present examples involving the 168-element group PSL2(7) = GL3(2) and the Mathieu group M24.