location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword $L$-functions

 Expand all        Collapse all Results 1 - 4 of 4

1. CJM 2016 (vol 68 pp. 908)

Sugiyama, Shingo; Tsuzuki, Masao
 Existence of Hilbert Cusp Forms with Non-vanishing $L$-values We develop a derivative version of the relative trace formula on $\operatorname{PGL}(2)$ studied in our previous work, and derive an asymptotic formula of an average of central values (derivatives) of automorphic $L$-functions for Hilbert cusp forms. As an application, we prove the existence of Hilbert cusp forms with non-vanishing central values (derivatives) such that the absolute degrees of their Hecke fields are arbitrarily large. Keywords:automorphic representations, relative trace formulas, central $L$-values, derivatives of $L$-functionsCategories:11F67, 11F72

2. CJM 2014 (vol 67 pp. 424)

Samart, Detchat
 Mahler Measures as Linear Combinations of $L$-values of Multiple Modular Forms We study the Mahler measures of certain families of Laurent polynomials in two and three variables. Each of the known Mahler measure formulas for these families involves $L$-values of at most one newform and/or at most one quadratic character. In this paper, we show, either rigorously or numerically, that the Mahler measures of some polynomials are related to $L$-values of multiple newforms and quadratic characters simultaneously. The results suggest that the number of modular $L$-values appearing in the formulas significantly depends on the shape of the algebraic value of the parameter chosen for each polynomial. As a consequence, we also obtain new formulas relating special values of hypergeometric series evaluated at algebraic numbers to special values of $L$-functions. Keywords:Mahler measures, Eisenstein-Kronecker series, $L$-functions, hypergeometric seriesCategories:11F67, 33C20

3. CJM 2013 (vol 65 pp. 1320)

Taniguchi, Takashi; Thorne, Frank
 Orbital $L$-functions for the Space of Binary Cubic Forms We introduce the notion of orbital $L$-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from their intrinsic interest, the results from this paper are used to prove the existence of secondary terms in counting functions for cubic fields. This is worked out in a companion paper. Keywords:binary cubic forms, prehomogeneous vector spaces, Shintani zeta functions, $L$-functions, cubic rings and fieldsCategories:11M41, 11E76

4. CJM 2001 (vol 53 pp. 1194)

Louboutin, Stéphane
 Explicit Upper Bounds for Residues of Dedekind Zeta Functions and Values of $L$-Functions at $s=1$, and Explicit Lower Bounds for Relative Class Numbers of $\CM$-Fields We provide the reader with a uniform approach for obtaining various useful explicit upper bounds on residues of Dedekind zeta functions of numbers fields and on absolute values of values at $s=1$ of $L$-series associated with primitive characters on ray class groups of number fields. To make it quite clear to the reader how useful such bounds are when dealing with class number problems for $\CM$-fields, we deduce an upper bound for the root discriminants of the normal $\CM$-fields with (relative) class number one. Keywords:Dedekind zeta functions, $L$-functions, relative class numbers, $\CM$-fieldsCategories:11R42, 11R29
 top of page | contact us | privacy | site map |