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Number Theory

Part of the Developments in Mathematics Book Series (volume 15)

Editors: Zhang, Wenpeng; Tanigawa, Yoshio

DOI: 10.1007/0-387-30829-6

ISBN: 978-0-387-30414-4

Publisher: Springer US - Springer Journals

Jan 1, 2006

1 - 10 of 16 Chapters

LitStream

Chapter 1Positive Finiteness of Number Systems

Akiyama, Shigeki

Pages: 1 –10

[We characterize the set of β’s for which each polynomial in β with nonnegative integer coefficients has a finite admissible expression in some number systems.]
LitStream

Chapter 2On a Distribution Property of the Residual Order of a (mod p)— IV

Chinen, Koji; Murata, Leo

Pages: 11 –22

[Let a be a positive integer and Qa (x; k, l) be the set of primes p≤x such that the residual order of a (mod p) in Z/pZ is congruent to l modulo k. In this paper, under the assumption of the Generalized Riemann Hypothesis, we prove that for any residue class l (mod k) the set Qa(x;k,l) has the...
LitStream

Chapter 3Diagonalizing “Bad” Hecke Operators on Spaces of Cusp Forms

Choie, YoungJu; Kohnen, Winfried

Pages: 23 –26

[We show that “bad” Hecke operators on space of newforms “often” can be diagonalized.]
LitStream

Chapter 4On the Hilbert-Kamke and the Vinogradov Problems in Additive Number Theory

Chubarikov, Vladimir N.

Pages: 27 –37

[This paper is survey on recent results on the system of equations x1s + ... + xks = βs, 1 ≤ s ≤ n, in natural number unknowns — the Hilbert-Kamke system, and one on prime unknowns — the Vinogradov system of equations. The main problem is to determine or estimate the Hardy-Littlewood function...
LitStream

Chapter 5The Goldbach-Vinogradov Theorem in Arithmetic Progressions

Cui, Zhen

Pages: 39 –65

[We prove that the ternary Goldbach problem can be solved with two of the prime variables in different arithmetic progressions.]
LitStream

Chapter 6Densities of Sets of Primes Related to Decimal Expansion of Rational Numbers

Hadano, Toshihiro; Kitaoka, Yoshiyuki; Kubota, Tomio; Nozaki, Michihiro

Pages: 67 –80

[For a prime p and a given integer a ≠ 0, ±1, not divisible by p, we suppose the order of a mod p is composite nk, n > 1. Let ri be the least non-negative residue mod p of aki, 0 ≤ i ≤ n — 1 (which has a relationship to a-adic expansion of 1/p), and let sa(p) = 1/pΣi=0n−1ri = Σi=0n−1 {aki/p},...
LitStream

Chapter 7Spherical Functions on p-Adic Homogeneous Spaces

Hironaka, Yumiko

Pages: 81 –95

[In §1, after defining spherical functions on homogeneous spaces, we examine the case of symmetric forms as an enlightening example. In §2, we introduce a general formula of spherical functions using functional equations under suitable assumption. In §3, we study a certain mechanism of functional...
LitStream

Chapter 8On Modular forms of Weight (6n + 1)/5 Satisfying a Certain Differential Equation

Kaneko, Masanobu

Pages: 97 –102

[We study solutions of a differential equation which arose in our previous study of supersingular elliptic curves. By choosing one fifth of an integer κ as the parameter involved in the differential equation, we obtain modular forms of weight k as solutions. It is observed that this solution is...
LitStream

Chapter 9Some Aspects of the Modular Relation

Kanemitsu, Shigeru; Tanigawa, Yoshio; Tsukada, Haruo; Yoshimoto, Masami

Pages: 103 –118

[This paper is a companion to the forthcoming paper [19] and exhibits various manifestations of the modular relation, equivalent to the functional equation. We shall give a somewhat new proof of the functinal equation for the Hurwitz-Lerch Dirichlet L-functions in §1, elucidation of Chan’s result...
LitStream

Chapter 10Zeros of Automorphic L-Functions and Noncyclic Base Change

Liu, Jianya; Ye, Yangbo

Pages: 119 –152

[Let π be an automorphic irreducible cuspidal representation of GLm over a Galois (not necessarily cyclic) extension E of ℚ of degree ℓ. We compute the n-level correlation of normalized nontrivial zeros of L(s, π). Assuming that π is invariant under the action of the Galois group Gal(E/ℚ), we...

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