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Experimental Mathematics, ISSN 1058-6458, 07/2016, Volume 25, Issue 3, pp. 295 - 319
For any square-free integer N such that the "moonshine group" Γ 0 (N) + has genus zero, the Monstrous Moonshine Conjectures relate the Hauptmodul of Γ 0 (N) +... 
Eisenstein series | Kronecker limit formula | Hauptmodul | q-expansions | MATHEMATICS | MOONSHINE | COEFFICIENTS
Journal Article
Annales mathématiques du Québec, ISSN 2195-4755, 4/2019, Volume 43, Issue 1, pp. 99 - 124
We develop two applications of the Kronecker’s limit formula associated to elliptic Eisenstein series... 
Algebra | Modular forms | Analysis | Mathematics, general | Eisenstein series | 11M36 | Mathematics | Number Theory | Kronecker limit formula | 11F11
Journal Article
Nagoya mathematical journal, ISSN 0027-7630, 09/2015, Volume 219, Issue 1, pp. 269 - 302
.... We then prove p-adic analogues of the first and second Kronecker limit formulas by using the distribution relation of the Kronecker theta function. 
POLYLOGARITHMS | INTERPOLATION | MATHEMATICS | COHOMOLOGY | SYNTOMIC REGULATORS | THETA-FUNCTIONS | 11G15 | Eisenstein–Kronecker series | distribution relation | 11G07 | 14G10 | 14F30 | Kronecker limit formula | Coleman’s p-adic integration | 11G55
Journal Article
Journal of Number Theory, ISSN 0022-314X, 10/2019, Volume 203, pp. 95 - 117
In this paper, we study twisted arithmetic divisors on the modular curve X0(N) with N square-free. For each pair (Δ,r), where Δ≡r2mod4N and Δ is a fundamental... 
Arithmetic intersection | Kronecker limit formula | Twisted arithmetic Siegel-Weil formula
Journal Article
Journal of Number Theory, ISSN 0022-314X, 04/2019, Volume 197, pp. 185 - 217
.... As an application, we present relative versions of the residue formula and Kronecker's limit formula for the “relative... 
Extension of number fields | Hecke's integral formula | Eisenstein series | Kronecker's limit formula | MATHEMATICS
Journal Article
American journal of mathematics, ISSN 1080-6377, 2017, Volume 139, Issue 4, pp. 1047 - 1084
The aim of this paper is to present a function field analogue of the classical Kronecker limit formula... 
Kronecker products | Functions | MATHEMATICS | Mathematics | Formulae | Fields, Algebraic | Research | Mathematical research | Integrals | Derivatives
Journal Article
Archiv der Mathematik, ISSN 0003-889X, 04/2016, Volume 106, Issue 4, pp. 327 - 335
.... it cannot be decomposed into the orthogonal sum of two non-zero sublattices. The proof is based on a formula found by Terras, which generalises Kronecker's limit formula... 
Euclidean lattice | Kronecker’s limit formula | Height | Quadratic form | Epstein’s zeta function | MATHEMATICS | ZETA-FUNCTION | Kronecker's limit formula | Epstein's zeta function | Mathematics | Number Theory
Journal Article
Journal of Number Theory, ISSN 0022-314X, 02/2020, Volume 207, pp. 315 - 348
... and its s-derivative. In particular, we obtain Kronecker limit formulas for ζ when restricted to points fixed by elements of G... 
Zeta integrals | Special values | Kronecker limit formulas | Lambert series | Multiple zeta functions | Multiple gamma function | MATHEMATICS | Mathematics - Number Theory
Journal Article
09/2013
Experimental Mathematics Volume 25, Issue 3, 2016, pages 295-320 For any square-free integer $N$ such that the "moonshine group" $\Gamma_0(N)^+$ has genus... 
Journal Article
Journal of Number Theory, ISSN 0022-314X, 01/2016, Volume 158, pp. 90 - 103
.... Then, we derive some interesting consequences for the class number of a quadratic imaginary number field K using Kronecker's limit formula and Hecke's formulation for the meromorphic continuation... 
Gauss problem | Riemann hypothesis | Kronecker's limit formula | Dedekind zeta function | Epstein zeta functions | MATHEMATICS | RIEMANN-HYPOTHESIS
Journal Article
by Du, TP and Yang, TH
JOURNAL OF NUMBER THEORY, ISSN 0022-314X, 10/2019, Volume 203, pp. 95 - 117
In this paper, we study twisted arithmetic divisors on the modular curve X-0(N) with N square-free. For each pair (Delta, r), where Delta equivalent to r(2)... 
MATHEMATICS | Arithmetic intersection | EISENSTEIN SERIES | TRACES | Twisted arithmetic Siegel-Weil formula | CM VALUES | Kronecker limit formula | POINTS | HEEGNER DIVISORS | DERIVATIVES | CURVES
Journal Article
Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 2007, Volume 37, Issue 1, pp. 109 - 117
We give a new proof of a formula of Bloch for a special value of a certain Eisenstein series of weight one with an additive character 
Dilogarithm | Elliptic curves | Kronecker limit formulas | 14G10 | elliptic curves | dilogarithm | 11G55
Journal Article
Research in Number Theory, ISSN 2363-9555, 12/2015, Volume 1, Issue 1, pp. 1 - 20
We establish a Kronecker limit formula for the zeta function ζ F (s,A) of a wide ideal class A of a totally real number field F of degree n... 
Heegner cycle | Mathematics | Number Theory | Maximal parabolic Eisenstein series | Kronecker limit formula | Transcendence
Journal Article
Resultate der Mathematik, ISSN 1420-9012, 2020, Volume 75, Issue 1
For a positive integer N, we derive a Kronecker type limit formula for a Dedekind type zeta function zeta OK(N... 
KLOOSTERMAN SUMS | MATHEMATICS | MATHEMATICS, APPLIED | quadratic orders | Chowla-Selberg formula | Kronecker limit formula | FORMULA | Dedekind zeta function
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2010, Volume 130, Issue 7, pp. 1642 - 1674
We obtain a “Kronecker limit formula” for the Epstein zeta function. This is done by introducing a generalized gamma function attached to the Epstein zeta function... 
“ [formula omitted]”-version | Bessel-zeta function | Epstein's zeta function | Kronecker's limit formula | Lerch's theorem | Generalized gamma function | "s=0" -version | MATHEMATICS | "s=0"-version
Journal Article
GAFA Geometric And Functional Analysis, ISSN 1016-443X, 12/2006, Volume 16, Issue 6, pp. 1291 - 1323
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2008, Volume 128, Issue 2, pp. 426 - 450
.... The main results are (1) a generalization of Zagier's formula for the constant term of the Laurent expansion at s = 1 , (2... 
Zeta and L-functions | Double sine functions | Kronecker limit formula | Real quadratic fields | MATHEMATICS
Journal Article
Pacific Journal of Mathematics, ISSN 0030-8730, 03/2006, Volume 224, Issue 1, pp. 185 - 200
We introduce a general method for obtaining the main zeta invariants for a class of double series of Dirichlet type and we apply it to the case of homogeneous... 
Kronecker limit formula | Zeta functions | Dirichlet series | MATHEMATICS | zeta functions | DETERMINANTS | SPHERES | FIELD | VALUES
Journal Article
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