The Number of Parts in Certain Residue Classes of Integer Partitions

We use the Circle Method to derive asymptotic formulas for functions related to the number of parts of partitions in particular residue classes.Comment: 16 pages, v3: fixed a typo in Theorem 1.3, added Example 1.4, and re-ordered reference

On the number of parts of integer partitions lying in given residue classes

Improving upon previous work on the subject, we use Wright's Circle Method to derive an asymptotic formula for the number of parts in all partitions of an integer that are in any given arithmetic progression.Comment: 10 page

Asymptotic formulae for partition ranks

Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann

Lacunary recurrences for Eisenstein series

Using results from the theory of modular forms, we reprove and extend a result of Romik about lacunary recurrence relations for Eisenstein series.Comment: 6 pages, more detailed proofs in v3, accepted for publication in Research in Number Theor

On class invariants for non-holomorphic modular functions and a question of Bruinier and Ono

Recently, Bruinier and Ono found an algebraic formula for the partition function in terms of traces of singular moduli of a certain non-holomorphic modular function. In this paper we prove that the rational polynomial having these singuar moduli as zeros is (essentially) irreducible, settling a question of Bruinier and Ono. The proof uses careful analytic estimates together with some related work of Dewar and Murty, as well as extensive numerical calculations of Sutherland

Special values of shifted convolution Dirichlet series

In a recent important paper, Hoffstein and Hulse generalized the notion of Rankin-Selberg convolution $L$-functions by defining shifted convolution $L$-functions. We investigate symmetrized versions of their functions. Under certain mild conditions, we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and "mixed mock modular" forms.Comment: 18 pages, corrected slight error in main theorem and made according minor edits in Sections 3.4 and 3.

Thieves In Cyberspace: Examining Music Piracy And Copyright Law Deficiencies In Russia As It Enters The Digital Age

The article discusses broadly the music piracy problem in Russia, the current state of Russia’s copyright laws, and how its laws and problems compare to the U.S. and the rest of the world. In particular, the article focuses on music piracy through the Internet and how it has exploded in Russia. One of the websites I target is the infamous Allofmp3.com, which has attracted a large amount of U.S. attention in recent times by consumers as well as lawmakers. The article analyzes the legislative and enforcement deficiencies in Russia that led to the enormous problem with traditional music piracy and that led to the rise of Internet piracy. The article also analyzes the recent attempt by international organizations to prosecute Allofmp3.com for copyright infringement and why that attempt failed. Finally, the article discusses what steps need to be taken by the United States and copyright owners to remedy the growing problem in Russia