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Search: All articles in the CMB digital archive with keyword L-function

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1. CMB 2015 (vol 59 pp. 119)

Hu, Pei-Chu; Li, Bao Qin
 A Simple Proof and Strengthening of a Uniqueness Theorem for L-functions We give a simple proof and strengthening of a uniqueness theorem for functions in the extended Selberg class. Keywords:meromorphic function, Dirichlet series, L-function, zero, order, uniquenessCategories:30B50, 11M41

2. CMB 2015 (vol 58 pp. 620)

Sands, Jonathan W.
 $L$-functions for Quadratic Characters and Annihilation of Motivic Cohomology Groups Let $n$ be a positive even integer, and let $F$ be a totally real number field and $L$ be an abelian Galois extension which is totally real or CM. Fix a finite set $S$ of primes of $F$ containing the infinite primes and all those which ramify in $L$, and let $S_L$ denote the primes of $L$ lying above those in $S$. Then $\mathcal{O}_L^S$ denotes the ring of $S_L$-integers of $L$. Suppose that $\psi$ is a quadratic character of the Galois group of $L$ over $F$. Under the assumption of the motivic Lichtenbaum conjecture, we obtain a non-trivial annihilator of the motivic cohomology group $H_\mathcal{M}^2(\mathcal{O}_L^S,\mathbb{Z}(n))$ from the lead term of the Taylor series for the $S$-modified Artin $L$-function $L_{L/F}^S(s,\psi)$ at $s=1-n$. Keywords:motivic cohomology, regulator, Artin L-functionsCategories:11R42, 11R70, 14F42, 19F27

3. CMB 2013 (vol 57 pp. 845)

Lei, Antonio
 Factorisation of Two-variable $p$-adic $L$-functions Let $f$ be a modular form which is non-ordinary at $p$. Loeffler has recently constructed four two-variable $p$-adic $L$-functions associated to $f$. In the case where $a_p=0$, he showed that, as in the one-variable case, Pollack's plus and minus splitting applies to these new objects. In this article, we show that such a splitting can be generalised to the case where $a_p\ne0$ using Sprung's logarithmic matrix. Keywords:modular forms, p-adic L-functions, supersingular primesCategories:11S40, 11S80

4. CMB 2013 (vol 57 pp. 381)

 On Complex Explicit Formulae Connected with the MÃ¶bius Function of an Elliptic Curve We study analytic properties function $m(z, E)$, which is defined on the upper half-plane as an integral from the shifted $L$-function of an elliptic curve. We show that $m(z, E)$ analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for $m(z, E)$ in the strip $|\Im{z}|\lt 2\pi$. Keywords:L-function, MÃ¶bius function, explicit formulae, elliptic curveCategories:11M36, 11G40