Journal ArticleProceedings of the American Mathematical Society · January 1, 2016
Langlands’ beyond endoscopy proposal for establishing functoriality motivates interesting and concrete problems in the representation theory of algebraic groups. We study these problems in a setting related to the Langlands L-functions L(s, π, ⊗3), where π ...
Full textCite
Journal ArticlePacific Journal of Mathematics · January 1, 2015
In this paper we prove a relative trace formula for all pairs of connected algebraic groups H ≤ G × G, with G a reductive group and H the direct product of a reductive group and a unipotent group, given that the test function satisfies simplifying hypothes ...
Full textCite
Journal ArticleRocky Mountain Journal of Mathematics · December 1, 2007
One of the main goals in this paper is to establish convolution sums of functions for the divisor sums σ̃s (n) = Σd/n (-1)d-1ds and σ̂ s = Σd/n(-l)(n/d)-1ds, for certain s, which were first defined by Glaisher. We first introduce three functions P(q), E(q), ...
Full textCite
Journal ArticleProceedings of the American Mathematical Society · August 1, 2007
Let Γ ≤ SL2(ℝ) be a genus zero Fuchsian group of the first kind with ∞ as a cusp, and let EΓ2k be the holomorphic Eisenstein series of weight 2k on Γ that is nonvanishing at ∞ and vanishes at all the other cusps (provided that such an Eisenstein series exi ...
Full textCite
Book · 2007
When seeking proofs of Ramanujan's identities for the Rogers–Ramanujan
functions, Watson, i.e., G. N. Watson, was not an “idiot.” He, L. J. ... functions. In
this paper, for 35 of the 40 identities, we offer proofs that are in the spirit of
Ramanuja ...
Cite
Journal ArticleJournal of Physics A: Mathematical and General · December 15, 2006
A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup Γ0(2) of the modular group SL2(ℤ) is constructed. These nonlinear equations are analogues of the well-known Ramanujan equations, as well as the Chazy ...
Full textCite
Journal ArticleMathematical Research Letters · January 1, 2002
In this article, we use functions studied by N. J. Fine and R. J. Evans to construct analogues of modular equations first discovered by S. Ramanujan. We then use these functions to construct new identities satisfied by Σn=0∞ p(ln+k)qn, with odd prime l and ...
Full textCite
