86 research outputs found
Equidistribution of signs for Hilbert modular forms of half-integral weight
We prove an equidistribution of signs for the Fourier coefficients of Hilbert
modular forms of half-integral weight. Our study focuses on certain subfamilies
of coefficients that are accessible via the Shimura correspondence. This is a
generalization of the result of Inam and Wiese to the setting of totally real
number fieldsComment: To appear in Research in Number Theor
An Alternative Approach to Computing
This paper presents a new approach to evaluating the special values of the
Dirichlet beta function, , where is any nonnegative integer.
Our approach relies on some properties of the Euler numbers and polynomials,
and uses basic calculus and telescoping series. By a similar procedure, we also
yield an integral representation of . The idea of our proof adapts
from a previous study by Ciaurri et al., where the authors introduced a new
proof of Euler's formula for .Comment: 11 page
Notes on the arithmetic of Hilbert modular forms
The purpose of this semi-expository article is to give another proof of a
classical theorem of Shimura on the critical values of the standard L-function
attached to a Hilbert modular form. Our proof is along the lines of previous
work of Harder and Hida (independently). What is different is an organizational
principle based on the period relations proved by Raghuram and Shahidi for
periods attached to regular algebraic cuspidal automorphic representations. The
point of view taken in this article is that one need only prove an algebraicity
theorem for the most interesting L-value, namely, the central critical value of
the L-function of a sufficiently general type of a cuspidal automorphic
representation. The period relations mentioned above then gives us a result for
all critical values. To transcribe such a result into a more classical context
we also discuss the arithmetic properties of the dictionary between holomorphic
Hilbert modular forms and automorphic representations of GL(2) over a totally
real number field F.Comment: To appear in the Journal of the Ramanujan Mathematical Societ
Arithmetic Properties of L-functions Attached to Hilbert Modular Forms
The goal of this thesis is to study some arithmetic properties of L-functions attached to Hilbert modular forms. We mainly use a representation theoretical point of view for the study, which can be done by associating Hilbert modular forms of our interests with automorphic representations of GL(2). Furthermore, their L-functions are deeply related. We use this realization to analyze the critical L-values for Hilbert modular forms, which reduces some technical difficulties. The thesis focuses on three main theorems which concern: Algebraicity theorem; Congruence property; and Non-vanishing property. The first theorem is completed by interpreting the Mellin transform cohomologically, and the second follows from analyzing it integrally. The third theorem is obtained by studying the completed L-functions of Hilbert modular forms.Department of Mathematic
Large Sums of Fourier Coefficients of Cusp Forms
Let be a fixed positive integer, and let be a primitive
cusp form given by the Fourier expansion . We consider the partial sum
. It is conjectured that
in the range . Lamzouri proved in arXiv:1703.10582
[math.NT] that this is true under the assumption of the Generalized Riemann
Hypothesis (GRH) for . In this paper, we prove that this conjecture
holds under a weaker assumption than GRH. In particular, we prove that given
and ,
we have in the range
provided that has no more than zeros in the
region for every real number with .Comment: 14 page
Physiological Studies on Dormancy of Strawberry (Fragaria grafidiflora EHRH. cultivar Hokowase) : II. Effect of Daytime Temperatures in the Period of Chilling Requirement on the Dormancy Breaking
SMAP2, a novel ARF GTPase-activating protein, interacts with clathrin and clathrin assembly protein and functions on the AP-1-positive early endosome/trans-Golgi network
Physiological Studies on Dormancy of Strawberry (Fsagaria grandiflora EHRH. cultivar Hokowase) : I. Growth Habit in the Period of Dormancy and Changes of Growth-Regulating Substances in the Crown with Progress of Dormancy
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