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Analytic number theory in India during 2001-2010 (Q2304126)

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Language	Label	Description	Also known as
English	Analytic number theory in India during 2001-2010	scientific article

Statements

scholarly article

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Analytic number theory in India during 2001-2010 (English)

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Ritabrata Munshi

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Indian Journal of Pure \& Applied Mathematics

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publication date

6 March 2020

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zbMATH Keywords

zeta function

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Diophantine equations

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additive combinatorics

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transcendental number theory

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s13226-019-0351-6

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Zero-sum problems with subgroup weights

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Remarks on some zero-sum theorems

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Visibility in the plane

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Some zero-sum constants with weights

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Davenport constant with weights and some related questions. II.

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Contributions to zero-sum problems

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On a question regarding visibility of lattice points. III.

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On the average of the sum-of-p-prime-divisors function

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Transcendental infinite sums

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On the number of Fourier coefficients that determine a Hilbert modular form

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On ideal-function-like functions.

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On an additive representation function.

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The Bohr inequality for ordinary Dirichlet series

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Asymptotic formula for sum-free sets in abelian groups

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On the exact degree of ℚ(√𝕒₁,√𝕒₂,…,√𝕒_{ℓ}) over ℚ

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On the Diophantine equation \(\frac{x^m-1}{x-1}=\frac{y^n-1}{y-1}\).

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Exponents of class groups of real quadratic function fields

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Exponents of class groups of real quadratic function fields (II)

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EXPONENTS OF CLASS GROUPS OF REAL QUADRATIC FIELDS

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Class numbers with many prime factors

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On the number of real quadratic fields with class number divisible by 3

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Manifestations of the Parseval identity

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On the values of a class of Dirichlet series at rational arguments

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The number of rational numbers determined by large sets of integers

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Note on Hermitian Jacobi forms

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Some aspects of Hermitian Jacobi forms

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NONVANISHING OF JACOBI POINCARÉ SERIES

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Positive integers whose Euler function is a power of their kernel function

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Determining modular forms on \(\text{SL}_2(\mathbb Z)\) by central values of convolution \(L\)-functions

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ON THE DIMENSION OF THE SPACE OF CUSP FORMS OF OCTAHEDRAL TYPE

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Integers without large prime factors in short intervals: conditional results

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On the structure of sequences with forbidden zero-sum subsequences

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Olson's constant for the group \(\mathbb Z_p\oplus\mathbb Z_p\)

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On the structure of \(p\)-zero-sum free sequences and its application to a variant of Erdős-Ginzburg-Ziv theorem

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On zero-sum sequences of prescribed length

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The sum involving derivative of \(\zeta(s)\) over simple zeros

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On the Zeros of Certain Cusp Forms

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TRANSCENDENTAL ZEROS OF CERTAIN MODULAR FORMS

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A canonical subspace of modular forms of half-integral weight

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On special values of certain Dirichlet \(L\)-functions

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On the representation of integers as sums of an odd number of squares

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Distribution of quadratic non-residues which are not primitive roots

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Distribution of residues modulo p

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On the Diophantine Equation <i>n</i>(<i>n</i> + <i>d</i>) · · · (<i>n</i> + (<i>k</i> − 1)<i>d</i>) = <i>by</i><sup><i>l</i></sup>

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An extension of a theorem of Euler

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THE FIRST NEGATIVE HECKE EIGENVALUE

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GAPS BETWEEN THE ZEROS OF EPSTEIN'S ZETA-FUNCTIONS ON THE CRITICAL LINE

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Nonvanishing of symmetric square $L$-functions of cusp forms inside the critical strip

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On quadratic character twists of Hecke L-functions attached to cusp forms of varying weights at the central point

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A certain class of Poincaré series on \(Sp_n\). II.

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On the average of central values of symmetric square <i>L</i>-functions in weight aspect

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On Koecher-Maass series of Siegel modular forms

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On the first sign change of Hecke eigenvalues of newforms

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The first negative Hecke eigenvalue of a Siegel cusp form of genus two

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Signs of Fourier coefficients of two cusp forms of different weights

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Number of prime divisors in a product of consecutive integers

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Number of prime divisors in a product of terms of an arithmetic progression

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The greatest prime divisor of a product of consecutive integers

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GRIMM'S CONJECTURE ON CONSECUTIVE INTEGERS

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The greatest prime divisor of a product of terms in an arithmetic progression

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The equation n(n+d) ⋅⋅⋅(n+(k-1)d)=by<sup>2</sup>with ω(d)≤6 or d≤10<sup>10</sup>

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Squares in arithmetic progression with at most two terms omitted

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Squares in products in arithmetic progression with at most one term omitted and common difference a prime power

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Irreducibility of generalized Hermite-Laguerre polynomials. II.

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ON A CONJECTURE ON RAMANUJAN PRIMES

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The average behavior of Fourier coefficients of cusp forms over sparse sequences

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Some results on Oppenheim's ``Factorisatio Numerorum'' function

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On the moments of the Carmichael λ function

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On positive integers \(n\) such that \(\varphi(1)+\varphi(2)+\cdots+ \varphi(n)\) is a square

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Diophantine equations with products of consecutive terms in Lucas sequences

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Diophantine equations with products of consecutive terms in Lucas sequences II

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On an arithmetic function considered by Pillai

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ON A CERTAIN GENERAL EXPONENTIAL SUM

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On certain exponential sums over primes

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The behaviour in short intervals of exponential sums over sifted integers

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EXPONENTIAL SUMS OVER PRIMES IN RESIDUE CLASSES

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On Shimura, Shintani and Eichler-Zagier correspondences

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An estimate for a certain average of the special values of character twists of modular $L$-functions

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An Eichler-Zagier map for Jacobi forms of half-integral weight

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On the mean square of standard \(L\)-functions attached to Ikeda lifts

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Almost squares in arithmetic progression (II)

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Almost squares in arithmetic progression. III

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A ZERO DENSITY ESTIMATE FOR THE SELBERG CLASS

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On the zeros of functions in the Selberg class

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Transcendental values of the digamma function

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Transcendental values of the p-adic digamma function

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SPECIAL VALUES OF THE POLYGAMMA FUNCTIONS

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On the uniform distribution of certain sequences

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The large sieve inequality for integer polynomial amplitudes

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The Large Sieve Inequality for Quadratic Polynomial Amplitudes

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On series, integrals and continued fractions, III

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On an asymptotic formula of Srinivasa Ramanujan

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A note on certain divisibility properties of the Fourier coefficients of normalized Eisenstein series

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On the Fourier expansions of Jacobi forms of half-integral weight

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Arithmetical applications of an identity for the Vandermonde determinant

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Arcs with no more than two integer points on conics

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ON DAVENPORT'S CONSTANT

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On a sum involving Fourier coefficients of cusp forms

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Higher moments of certain \(L\)-functions on the critical line

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ESTIMATES FOR THE SOLUTIONS OF CERTAIN DIOPHANTINE EQUATIONS BY RUNGE'S METHOD

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Omega theorems for a class of \(L\)-functions. (A note on the Rankin-Selberg zeta-function)

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Zero-density estimate of L-functions attached to Maass forms

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Almost perfect powers in arithmetic progression

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Some extensions and refinements of a theorem of Sylvester

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ON THE TRANSCENDENCE OF INFINITE SUMS OF VALUES OF RATIONAL FUNCTIONS

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Contributions towards a conjecture of Erdos on perfect powers in arithmetic progression

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Solutions of some generalized Ramanujan-Nagell equations

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On the equation n(n+d)⋅⋅⋅(n+(i<sub>0</sub>-1)d)(n+(i<sub>0</sub>+1)d)⋅⋅⋅(n+(k-1)d)=y<sup>l</sup>with 0<i<sub>0</sub><k-1

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Arithmetic progressions with common difference divisible by small primes

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Almost perfect powers in consecutive integers. II

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Distinguishing Hecke eigenvalues of primitive cusp forms

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Gao's conjecture on zero-sum sequences.

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Distinct zeros of functions in the Selberg class

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A lower bound for certain Ramsey type problems

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Adams theorem on Bernoulli numbers revisited

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A variant of Davenport's constant

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Identifiers

zbMATH Open document ID

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10.1007/s13226-019-0351-6

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2304126

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