Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Fréchette, Claire"'
Autor:
Browning, Thomas L., Čoupek, Pavel, Eischen, Ellen, Frechette, Claire, Hong, Serin, Lee, Si Ying, Marcil, David
We introduce a method for producing vector-valued automorphic forms on unitary groups from scalar-valued ones. As an application, we construct an explicit example. Our strategy employs certain differential operators. It is inspired by work of Cl\'ery
Externí odkaz:
http://arxiv.org/abs/2408.05198
Given a multiplicative function $f$, we let $S(x,f)=\sum_{n\leq x}f(n)$ be the associated partial sum. In this note, we show that lower bounds on partial sums of divisor-bounded functions result in lower bounds on the partial sums associated to their
Externí odkaz:
http://arxiv.org/abs/2405.00658
Let $N$ be a fixed positive integer, and let $f\in S_k(N)$ be a primitive cusp form given by the Fourier expansion $f(z)=\sum_{n=1}^{\infty} \lambda_f(n)n^{\frac{k-1}{2}}e(nz)$. We consider the partial sum $S(x,f)=\sum_{n\leq x}\lambda_f(x)$. It is c
Externí odkaz:
http://arxiv.org/abs/2308.06311
Whittaker functions are special functions that arise in $p$-adic number theory and representation theory. They may be defined on representations of reductive groups as well as their metaplectic covering groups: fascinatingly, many of their number the
Externí odkaz:
http://arxiv.org/abs/2301.02223
Autor:
Curran, Michael J., Frechette, Claire, Yost-Wolff, Calvin, Zhang, Sylvester W., Zhang, Valerie
We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock space, we prove a Cauchy identity for super LLT poly
Externí odkaz:
http://arxiv.org/abs/2110.07597
Autor:
Frechette, Claire
In this paper, we extend results connecting quantum groups to spherical Whittaker functions on metaplectic covers of $GL_r(F)$, for $F$ a nonarchimedean local field. Brubaker, Buciumas, and Bump showed that for a certain metaplectic $n$-fold cover of
Externí odkaz:
http://arxiv.org/abs/2009.13669
We introduce families of two-parameter multivariate polynomials indexed by pairs of partitions $v,w$ -- biaxial double $(\beta,q)$-Grothendieck polynomials -- which specialize at $q=0$ and $v=1$ to double $\beta$-Grothendieck polynomials from torus-e
Externí odkaz:
http://arxiv.org/abs/2007.04310
Autor:
Beneish, Lea, Frechette, Claire
Publikováno v:
Journal of Number Theory. Volume 168, November 2016, Pages 413-432
In this paper, we study the parallel cases of Zagier's and Folsom-Ono's grids of weakly holomorphic (resp. weakly holomorphic and mock modular) forms of weights 3/2 and 1/2, investigating their $p$-adic properties under the action of Hecke operators.
Externí odkaz:
http://arxiv.org/abs/1509.00383
Autor:
Frechette, Claire, Locus, Madeline
Publikováno v:
Ann. Comb. 20 (2016), 345--360
Here we consider the $q$-series coming from the Hall-Littlewood polynomials, \begin{equation*} R_\nu(a,b;q)=\sum_{\substack{\lambda \\[1pt] \lambda_1\leq a}} q^{c|\lambda|} P_{2\lambda}\big(1,q,q^2,\dots;q^{2b+d}\big). \end{equation*} These series we
Externí odkaz:
http://arxiv.org/abs/1407.2880
Autor:
Beneish, Lea, Frechette, Claire
Publikováno v:
In Journal of Number Theory November 2016 168:413-432
