scientific article

Publication date: 18 February 2011

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

Lagrange's theorem sum of eight squares Jacobi's formula Legendre's formula Girard-Fermat theorem Liouville's method recurrence relation for the sum of divisors function sum of four triangular numbers

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Theta series; Weil representation; theta correspondences (11F27) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01) Elementary number theory (11Axx)

Related Items (54)

The convolution sum $\sum_{al+bm=n} \sigma(l) \sigma(m)$ for $(a,b)=(1,28), (4,7), (1,14), (2,7), (1,7)$ ⋮ Arithmetic convolution sums derived from eta quotients related to divisors of 6 ⋮ Arithmetic identities associated with quadratic forms and their applications ⋮ ARITHMETIC SUMS OF LIOUVILLE TYPE OVER RELATIVELY PRIME PAIRS ⋮ Note on an analogue of Fermat's two squares theorem for primes p ≡ 3(mod8) ⋮ Evaluation of Convolution Sums entailing mixed Divisor Functions for a Class of Levels ⋮ On the problem σod(n) = σod(n+1) ⋮ The partition-frequency enumeration matrix ⋮ Analytic and arithmetic methods in Liouville's identities ⋮ Unnamed Item ⋮ Bernoulli numbers and certain convolution sums with divisor functions ⋮ A STUDY OF COFFICIENTS DERIVED FROM ETA FUNCTIONS ⋮ On some results of Hurwitz and Deutsch about certain quadratic forms ⋮ Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56 ⋮ Eisenstein series and their applications to some arithmetic identities and congruences ⋮ A simple extension of Ramanujan-Serre derivative map and some applications ⋮ On the number of representations of n as a linear combination of four triangular numbers II ⋮ Evaluation of some convolution sums and representation of integers by certain quadratic forms in 12 variables ⋮ Unnamed Item ⋮ The power series expansion of certain infinite products \newline $q^{r}\prod_{n=1}^{\infty}(1-q^{n})^{a_{1}}(1-q^{2n})^{a_{2}}\cdots(1-q^{mn})^{a_{m}}$ ⋮ Unnamed Item ⋮ Ramanujan’s theta functions and sums of triangular numbers ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Bernoulli identities and combinatoric convolution sums with odd divisor functions ⋮ TRANSFORMATION FORMULAS FOR THE NUMBER OF REPRESENTATIONS OF BY LINEAR COMBINATIONS OF FOUR TRIANGULAR NUMBERS ⋮ Jacobi's four-square theorem and the zeta function of Hurwitz quaternions ⋮ Proofs of some conjectures of Z.-H. Sun on relations between sums of squares and sums of triangular numbers ⋮ On the number of representations of certain quadratic forms in 20 and 24 variables ⋮ Theta products and eta quotients of level 24 and weight 2 ⋮ Evaluation of some $q$-integrals in terms of the Dedekind eta function ⋮ Convolution identities for twisted Eisenstein series and twisted divisor functions ⋮ Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52 ⋮ Sums of Liouville type over primitive pairs and quadruples and some integer representations ⋮ Evaluation of a certain combinatorial convolution sum in higher level cases ⋮ Unnamed Item ⋮ Liouville identities with two functions ⋮ On the number of representations of n as a linear combination of four triangular numbers ⋮ Convolution sums of a divisor function for prime levels ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Arithmetic properties derived from coefficients of certain eta quotients ⋮ Some relations between $t(a,b,c,d;n)$ and $N(a,b,c,d;n)$ ⋮ Some result for binomial convolution sums of restricted divisor functions ⋮ Restricted sums of four squares ⋮ THE REPRESENTATION NUMBERS OF CERTAIN OCTONARY QUADRATIC FORMS ⋮ On the number of representations of certain quadratic forms in 8 variables ⋮ INDUCTIVE FORMULAS FOR SOME ARITHMETIC FUNCTIONS ⋮ Differential equations involving cubic theta functions and Eisenstein series ⋮ Relations among representations of integers by certain quadratic forms ⋮ Evaluation of some sums of polynomials in $\mathbb{F}_q [t$] ⋮ REPRESENTATION NUMBERS OF TWO OCTONARY QUADRATIC FORMS ⋮ A three-term identity for products of three theta functions

This page was built for publication: