Note on Fields of Small Discriminant

On the Existence of Large Degree Galois Representations for Fields of Small Discriminant

Let L/K be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of Gal(L/K), the sharper of which is conditional on the Artin Conjecture and the Generalized Riemann Hypothesis. Our bound is nontrivial when [K : Q] is small and L has small root discriminant, and might be summarized as saying that such fields can’t...

the effects of cognitive strategies- note making and underlining- on iranian efl learners’ reading comprehension

هدف از انجام این مطالعه ، بررسی اثرات استفاده از استراتژی های شناختی یعنی "نت برداری" و "زیر خط کردن" بر روی عملکرد درک مطلب زبان آموزان ایرانی می باشد. به این منظور، 60 زبان آموز دختر سال چهارم دبیرستان از طریق آزمون پیشرفت زبان انگلیسی (نلسون)، از یک جامعه آماری بزرگتر انتخاب شدند. سپس به صورت تصادفی به سه گروه که هر گروه شامل ?0 دانش آموز همسان بود، تقسیم شدند: دو گروه آزمایش(گروه "نت برداری...

Septic fields with discriminant +- 2a3b

Septic Fields with Discriminant ±23

We classify septic number fields which are unramified outside of {∞, 2, 3} by a targeted Hunter search; there are exactly 10 such fields, all with Galois group S7. We also describe separate computations which strongly suggest that none of these fields come from specializing septic genus zero three-

A note on generators of number fields

We establish upper bounds for the smallest height of a generator of a number field k over the rational field Q. Our first bound applies to all number fields k having at least one real embedding. We also give a second conditional result for all number fields k such that the Dedekind zeta-function associated to the Galois closure of k/Q satisfies GRH. This provides a partial answer to a question ...