Zobrazeno 1 - 10
of 42
pro vyhledávání: '"11F37, 11F11"'
Autor:
Lovejoy, Jeremy, Osburn, Robert
We prove general fomulas for the deviations of two overpartition ranks from the average. These formulas are in terms of Appell--Lerch series and sums of quotients of theta functions and can be used, among other things, to recover any of the numerous
Externí odkaz:
http://arxiv.org/abs/2307.03418
Autor:
Zhu, Xiao-Jie
We study Taylor expansions of Jacobi forms of lattice index. As the main result, we give an embedding from certain space of such forms, whether scalar-valued or vector-valued, integral-weight or half-integral-weight, of any level, with any character,
Externí odkaz:
http://arxiv.org/abs/2204.08262
Autor:
Banerjee, Soumyarup
In this paper, we investigate sums of four squares of integers whose prime factorizations are restricted, making progress towards a conjecture of Sun that states that two of the integers may be restricted to the forms $2^a3^b$ and $2^c5^d$. We obtain
Externí odkaz:
http://arxiv.org/abs/2202.04057
Autor:
Roehrig, Christina, Zwegers, Sander
We generalize the construction from arXiv:2102.09329 of theta series for quadratic forms of signature $(n-1,1)$ with homogeneous and spherical polynomials. Namely, we allow that the parameters $c_1,c_2$, which define the theta series and ensure the c
Externí odkaz:
http://arxiv.org/abs/2201.03986
Autor:
Banerjee, Soumyarup, Kane, Ben
In this paper we study quadratic forms which are universal when restricted to almost prime inputs, establishing finiteness theorems akin to the Conway--Schneeberger 15 theorem.
Externí odkaz:
http://arxiv.org/abs/2106.05107
Autor:
Bringmann, Kathrin, Kane, Ben
We investigate the inner product between meromorphic modular forms from certain distinguished subspaces. In particular, we compute the degenerate parts of these subspaces and further compute the inner product on some of the remaining quotient spaces.
Externí odkaz:
http://arxiv.org/abs/2008.02210
Here we study the recently introduced notion of a locally harmonic Maass form and its applications to the theory of $L$-functions. In particular, we find finite formulas for certain twisted central $L$-values of a family of elliptic curves in terms o
Externí odkaz:
http://arxiv.org/abs/1803.10555
Autor:
Kane, Ben, Liu, Jingbo
In this paper we study universal quadratic polynomials which arise as sums of polygonal numbers. Specifically, we determine an asymptotic upper bound (as a function of $m$) on the size of the set $S_m\subset\mathbb{N}$ such that if a sum of $m$-gonal
Externí odkaz:
http://arxiv.org/abs/1802.08374
Autor:
Bringmann, Kathrin, Kane, Ben
The study of Fourier coefficients of meromorphic modular forms dates back to Ramanujan, who, together with Hardy, studied the reciprocal of the weight 6 Eisenstein series. Ramanujan conjectured a number of further identities for other meromorphic mod
Externí odkaz:
http://arxiv.org/abs/1603.07079
Autor:
Bhattacharya, Soumya
We show that a holomorphic eta quotient has only finitely many factors. We also provide an algorithm for checking irreducibility of holomorphic eta quotients by constructing an upper bound for the minimum of the levels of the proper factors of a redu
Externí odkaz:
http://arxiv.org/abs/1602.03087