Zobrazeno 1 - 10
of 236
pro vyhledávání: '"Rolen, Larry"'
We study zero attractors for polynomials built from partition statistics, complementing earlier work in this direction by Boyer, Goh, Parry, and others. In particular, using analytic methods we establish the zero attractor of partition $t$-hook polyn
Externí odkaz:
http://arxiv.org/abs/2408.16902
Given the L-series of a half-integral weight cusp form, we construct a cohomology class with coefficients in a finite dimensional vector space in a way that parallels the Eichler cohomology in the integral weight case. We also define a lift of half-i
Externí odkaz:
http://arxiv.org/abs/2307.10863
In this paper, we characterize the vanishing of twisted central $L$-values attached to newforms of square-free level in terms of so-called local polynomials and the action of finitely many Hecke operators thereon. Such polynomials are the ``local par
Externí odkaz:
http://arxiv.org/abs/2306.15519
In 1986, Andrews [2,3] studied the function $\sigma(q)$ from Ramanujan's "Lost" Notebook, and made several conjectures on its Fourier coefficients $S(n)$, which count certain partition ranks. In 1988, Andrews-Dyson-Hickerson [5] famously resolved the
Externí odkaz:
http://arxiv.org/abs/2305.16654
For a random partition, one of the most basic questions is: what can one expect about the parts which arise? For example, what is the distribution of the parts of random partitions modulo $N$? Since most partitions contain a $1$, and indeed many $1$s
Externí odkaz:
http://arxiv.org/abs/2305.02928
Using equidistribution criteria, we establish divisibility by cyclotomic polynomials of several partition polynomials of interest, including $spt$-crank, overpartition pairs, and $t$-core partitions. As corollaries, we obtain new proofs of various Ra
Externí odkaz:
http://arxiv.org/abs/2209.15114
Recently, much attention has been given to various inequalities among partition functions. For example, Nicolas, {and later DeSavlvo--Pak,} proved that $p(n)$ is eventually log-concave, and Ji--Zang showed that the cranks are eventually unimodal. Thi
Externí odkaz:
http://arxiv.org/abs/2209.12239
We define an analogue of the Bol operator on spaces of weakly holomorphic modular forms of half-integral weight. We establish its main properties and relation with other objects.
Externí odkaz:
http://arxiv.org/abs/2207.07057
A number of recent papers have estimated ratios of the partition function $p(n-j)/p(n)$, which appears in many applications. Here, we prove an easy-to-use effective bound on these ratios. Using this, we then study second shifted difference of partiti
Externí odkaz:
http://arxiv.org/abs/2203.11608
Autor:
Diamantis, Nikolaos, Rolen, Larry
Bruinier, Funke, and Imamoglu have proved a formula for what can philosophically be called the "central $L$-value" of the modular $j$-invariant. Previously, this had been heuristically suggested by Zagier. Here, we interpret this "$L$-value" as the v
Externí odkaz:
http://arxiv.org/abs/2201.10193