A variant of the Hardy-Ramanujan theorem

A proof of the Hardy - Ramanujan formulaDan

a comparative study of the theme of "marriage" in three victorian novelists: charles dickens, george eliot and thomas hardy

این تحقیق کوشیده است با انتخاب پنج رمان از میان آثار برگزیده، «چارلز دیکنز»، «جورج الیوت» و «توماس هاردی » و با رویکردی تطبیقی به بررسی درونمایه ی «ازدواج» در آثار این سه رمان نویس بزرگ دوره ی ویکتوریا بپردازد. فرضیه ی اولیه ی تحقیق این بوده است که چارلز دیکنز (1870- 1812) با زبانی شوخ و گزنده، جورج الیوت(1880- 1819) با نگاهی آموزشی–اندرزگونه و توماس هاردی(1928- 1840) با رویکردی تلخ وانتقادی به...

Efficient implementation of the Hardy{--}Ramanujan{--}Rademacher formula

We describe how the Hardy–Ramanujan–Rademacher formula can be implemented to allow the partition function p(n) to be computed with softly optimal complexity O(n) and very little overhead. A new implementation based on these techniques achieves speedups in excess of a factor 500 over previously published software and has been used by the author to calculate p(10), an exponent twice as large as i...

A Derivation of the Hardy-ramanujan Formula from an Arithmetic Formula

We re-prove the Hardy-Ramanujan asymptotic formula for the partition function without using the circle method. We derive our result from recent work of Bruinier and Ono on harmonic weak Maass forms.

A Variant of the Hales-jewett Theorem

It was shown by V. Bergelson that any set B ⊆ N with positive upper multiplicative density contains nicely intertwined arithmetic and geometric progressions: For each k ∈ N there exist a, b, d ∈ N such that ̆ b(a + id) : i, j ∈ {1, 2, . . . , k} ̄ ⊆ B. In particular one cell of each finite partition of N contains such configurations. We prove a Hales-Jewett type extension of this partition theorem.