159 research outputs found
Asymptotic behaviors of means of central values of automorphic -functions for GL(2)
Let be the adele ring of a totally real algebraic number field
. We push forward an explicit computation of a relative trace formula for
periods of automorphic forms along a split torus in from a square free
level case done by Masao Tsuzuki, to an arbitrary level case. By using a
relative trace formula, we study central values of automorphic -functions
for cuspidal automorphic representations of corresponding
to Maass forms with arbitrary level.Comment: 33 pages. Misprints are modifie
An explicit trace formula of Jacquet-Zagier type for Hilbert modular forms
We give an exact formula of the average of adjoint -functions of
holomorphic Hilbert cusp forms with a fixed weight and a square-free level,
which is a generalization of Zagier's formula known for the case of elliptic
cusp forms on . As an application, we prove that the
Satake parameters of Hilbert cusp forms with a fixed weight and with growing
square-free levels are equidistributed in an ensemble constructed by values of
the adjoint -functions
Existence of Hilbert cusp forms with non-vanishing -values
We give a derivative version of the relative trace formula on PGL(2) studied
in our previous work, and obtain a formula of an average of central values
(derivatives) of automorphic -functions for Hilbert cusp forms. As an
application, we prove existence of Hilbert cusp forms with non-vanishing
central values (derivatives) such that the absolute degrees of their Hecke
fields are sufficiently large
A quantum probabilistic approach to Hecke algebras for -adic
The subject of the present paper is an application of quantum probability to
-adic objects. We give a quantum-probabilistic interpretation of the
spherical Hecke algebra for , where is a -adic field. As
a byproduct, we obtain a new proof of the Fourier inversion formula for
Quantitative non-vanishing of central values of certain -functions on
Let be an even Hecke-Maass cusp form on whose
-function does not vanish at the center of the functional equation. In this
article, we obtain an exact formula of the average of triple products of
, and , where runs over an orthonormal basis of
Hecke eigen elliptic cusp forms on of a fixed weight
. As an application, we prove a quantitative non-vanishing results on
the central values for the family of degree -functions with in the union of as
.Comment: We improved our non-vanishing results in our previous manuscript. In
accordance with improvement, the title and abstract of the manuscript were
changed. Some typos are correcte
Optimal estimates for an average of Hurwitz class numbers
In this paper, we give an optimal estimate of an average of Hurwitz class
numbers. As an application, we give an equidistribution result of the family
with prime, weighted by Hurwitz class numbers. This
equidistribution produces many asymptotic relations among Hurwitz class
numbers. Our proof relies on the resolvent trace formula of Hecke operators on
elliptic cusp forms of weight
The limit theorem with respect to the matrices on non-backtracking paths of a graph
We give a limit theorem with respect to the matrices related to
non-backtracking paths of a regular graph. The limit obtained closely resembles
the th moments of the arcsine law. Furthermore, we obtain the asymptotics of
the averages of the th Fourier coefficients of the cusp forms related to
the Ramanujan graphs defined by A. Lubotzky, R. Phillips and P. Sarnak
Lattice sums of -Bessel functions, theta functions, linear codes and heat equations
We extend a certain type of identities on sums of -Bessel functions on
lattices, previously given by G. Chinta, J. Jorgenson, A Karlsson and M.
Neuhauser. Moreover we prove that, with continuum limit, the transformation
formulas of theta functions such as the Dedekind eta function can be given by
-Bessel lattice sum identities with characters. We consider analogues of
theta functions of lattices coming from linear codes and show that sums of
-Bessel functions defined by linear codes can be expressed by complete
weight enumerators. We also prove that -Bessel lattice sums appear as
solutions of heat equations on general lattices. As a further application, we
obtain an explicit solution of the heat equation on whose
initial condition is given by a linear code
Synthesis and application of a ¹⁹F-labeled fluorescent nucleoside as a dual-mode probe for i-motif DNAs
Because of their stable orientations and their minimal interference with native DNA interactions and folding, emissive isomorphic nucleoside analogues are versatile tools for the accurate analysis of DNA structural heterogeneity. Here, we report on a bifunctional trifluoromethylphenylpyrrolocytidine derivative (FPdC) that displays an unprecedented quantum yield and highly sensitive ¹⁹F NMR signal. This is the first report of a cytosine-based dual-purpose probe for both fluorescence and ¹⁹F NMR spectroscopic DNA analysis. FPdC and FPdC-containing DNA were synthesized and characterized; our robust dual probe was successfully used to investigate the noncanonical DNA structure, i-motifs, through changes in fluorescence intensity and ¹⁹F chemical shift in response to i-motif formation. The utility of FPdC was exemplified through reversible fluorescence switching of an FPdC-containing i-motif oligonucleotide in the presence of Ag(I) and cysteine
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