# Gautami Bhowmik - LPP

## Publications Authored By Gautami Bhowmik

Assuming a conjecture on distinct zeros of Dirichlet L-functions we get asymptotic results on the average number of representations of an integer as the sum of two primes in arithmetic progression. On the other hand the existence of good error terms gives information on the the location of zero free regions of L-functions and possible Siegel zeros. Similar results are obtained for an integer in a congruence class expressed as the sum of two primes. Read More

Let $G$ be a finite abelian group. We show that its Davenport constant $D(G)$ satisfies $D(G)\leq \exp(G)+\frac{|G|}{\exp(G)}-1$, provided that $\exp(G)\geq\sqrt{|G|}$, and $D(G)\leq 2\sqrt{|G|}-1$, if $\exp(G)<\sqrt{|G|}$. This proves a conjecture by Balasubramanian and the first named author. Read More

**Affiliations:**

^{1}LPP

**Category:**Mathematics - Number Theory

We study the natural boundary of a random Dirichlet series associated with Goldbach numbers. Read More

**Affiliations:**

^{1}LPP

**Category:**Mathematics - Number Theory

We consider the Dirichlet series associated to the number of representations of an integer as the sum of primes. Assuming the Riemann hypothesis on the distribution of the zeros of the Riemann zeta function we obtain the domain of meromorphic continuation of this series. Read More

**Affiliations:**

^{1}LPP

**Category:**Mathematics - Number Theory

This is an expository paper on the meromorphic continuation of zeta functions with Euler products (for example zeta functions of groups and height zeta functions) or without (for example the Goldbach zeta function). As an application we show how a natural boundary of analytic continuation can give asymptotic results. Read More

**Affiliations:**

^{1}LPP

**Category:**Mathematics - Number Theory

We classify singularities of Dirichlet series having Euler products which are rational functions for p and p^{-s} for p a prime number and give examples of natural boundaries from zeta functions of groups and height zeta functions. Read More

Let n be an integer, and consider finite sequences of elements of the group Z/nZ x Z/nZ. Such a sequence is called zero-sum free, if no subsequence has sum zero. It is known that the maximal length of such a zero-sum free sequence is 2n-2, and Gao and Geroldinger conjectured that every zero-sum free sequence of this length contains an element with multiplicity at least n-2. Read More

**Affiliations:**

^{1}LPP

**Category:**Mathematics - Number Theory

Assuming the Riemann Hypothesis we obtain asymptotic estimates for the mean value of the number of representations of an integer as a sum of two primes. By proving a corresponding Omega-term, we prove that our result is essentially the best possible. Read More

**Affiliations:**

^{1}LPP

**Category:**Mathematics - Number Theory

For a prime number p greater than 6000, the Olson's constant for the group Z_p+Z_p is given by Ol(Z_p+Z_p)=p-1+Ol(Z_p). Read More

**Affiliations:**

^{1}LPP,

^{2}DMA

**Category:**Mathematics - Number Theory

Let A be a zero-sum free subset of Z_n with |A|=k. We compute for k\le 7 the least possible size of the set of all subset-sums of A. Read More

**Affiliations:**

^{1}LPP,

^{2}DMA

We obtain a decidability result for the Davenport constant. Read More

We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results. Read More

**Affiliations:**

^{1}LPP

**Category:**Mathematics - Number Theory

We determine Davenport's constant for all groups of the form $\Z\_3\oplus \Z\_3\oplus\Z\_{3d}$. Read More

**Affiliations:**

^{1}Stockholm University,

^{2}Universite de Lille 1

We establish correspondances between factorisations of finite abelian groups (direct factors, unitary factors, non isomorphic subgroup classes) and factorisations of integer matrices. We then study counting functions associated to these factorisations and find average orders. Read More

**Affiliations:**

^{1}MATSCIENCE,

^{2}LPP

**Category:**Mathematics - Number Theory

We prove that for all but a certain number of abelian groups of order n its Davenport constant is atmost n/k+k-1 for k=1,2,..,7. Read More

**Affiliations:**

^{1}Laboratoire Paul PainlevĂ‰,

^{2}LMNO,

^{3}Rochester, NY, USA

**Category:**Mathematics - Number Theory

This article extends classical one variable results about Euler products defined by integral valued polynomial or analytic functions to several variables. We show there exists a meromorphic continuation up to a presumed natural boundary, and also give a criterion, a la Estermann-Dahlquist, for the existence of a meromorphic extension to $\C^n.$ Among applications we deduce analytic properties of height zeta functions for toric varieties over $\Q$ and group zeta functions. Read More