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

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

Algebra | Modular forms | Analysis | Mathematics, general | Eisenstein series | 11M36 | Mathematics | Number Theory | Kronecker limit formula | 11F11

Journal Article

3.
Full Text
p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas

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

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

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

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

Kronecker products | Functions | MATHEMATICS | Mathematics | Formulae | Fields, Algebraic | Research | Mathematical research | Integrals | Derivatives

Journal Article

Journal of Number Theory, ISSN 0022-314X, 06/2013, Volume 133, Issue 6, pp. 2092 - 2120

We revisit class number formulas, “s=0”-version of Kroneckerʼs limit formulas and Chowla...

Second gamma function with a character | Dedekindʼs zeta function | “[formula omitted]” version of Kroneckerʼs limit formula | Kummerʼs formula for the second gamma function with a character | Chowla–Selberg formula | m-th gamma function with a character | Cyclotomic field | Class number formula | Heckeʼs formula | Chowla-Selberg formula | "s = 0" version of Kronecker's limit formula | Kummer's formula for the second gamma function with a character | Dedekind's zeta function | M-th gamma function with a character | Hecke's formula | MATHEMATICS | "s=0" version of Kronecker's limit formula | REAL QUADRATIC FIELDS

Second gamma function with a character | Dedekindʼs zeta function | “[formula omitted]” version of Kroneckerʼs limit formula | Kummerʼs formula for the second gamma function with a character | Chowla–Selberg formula | m-th gamma function with a character | Cyclotomic field | Class number formula | Heckeʼs formula | Chowla-Selberg formula | "s = 0" version of Kronecker's limit formula | Kummer's formula for the second gamma function with a character | Dedekind's zeta function | M-th gamma function with a character | Hecke's formula | MATHEMATICS | "s=0" version of Kronecker's limit formula | REAL QUADRATIC FIELDS

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

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

ACTA ARITHMETICA, ISSN 0065-1036, 2019, Volume 191, Issue 4, pp. 309 - 340

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

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

Gauss problem | Riemann hypothesis | Kronecker's limit formula | Dedekind zeta function | Epstein zeta functions | MATHEMATICS | RIEMANN-HYPOTHESIS

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 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

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

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

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

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

“ [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

.... We prove the holomorphic factorization formula $$ \frac{{\det '\Delta _{n} }} {{\det N_{n} }} = c_{{g,n}} \exp {\left\{ { - \frac{{6n^{2} - 6n + 1}} {{12\pi }}S} \right...

58J52 | Green’s function | 32G15 (Secondary) | 11M36 (Primary) 14H15 | Mathematics | Kronecker limit formula | 30F10 | Dedekind eta function | Schottky space | Analysis | Liouville action | determinant of Laplacian | Schottky group | Teichmüller space | Dedkind eta function | Green's function | Determinant of Laplacian | INDEX THEOREM | SERIES | SCHOTTKY | SPACES | KLEINIAN-GROUPS | MATHEMATICS | Teichmuller space | ANALYTIC-TORSION | MANIFOLDS | Lionville action | OPERATORS | CUSP FORMS

58J52 | Green’s function | 32G15 (Secondary) | 11M36 (Primary) 14H15 | Mathematics | Kronecker limit formula | 30F10 | Dedekind eta function | Schottky space | Analysis | Liouville action | determinant of Laplacian | Schottky group | Teichmüller space | Dedkind eta function | Green's function | Determinant of Laplacian | INDEX THEOREM | SERIES | SCHOTTKY | SPACES | KLEINIAN-GROUPS | MATHEMATICS | Teichmuller space | ANALYTIC-TORSION | MANIFOLDS | Lionville action | OPERATORS | CUSP FORMS

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

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

Kronecker limit formula | Zeta functions | Dirichlet series | MATHEMATICS | zeta functions | DETERMINANTS | SPHERES | FIELD | VALUES

Journal Article

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